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Analyzing vertical asymptotes of rational functions | High School Math | Khan Academy

Video vocabulary

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

expression

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US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

rational

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US / 'ræʃnəl /

UK / ˈræʃənəl /

A2
  • adjecitve
  • Able to think clearly

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

vertical

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US / ˈvɜ:tɪkl /

UK / ˈvɜ:rtɪkl /

B1
  • adjecitve
  • (Of a line, etc.) going up and down; not horizontal

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

open

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US / 'əʊpən /

UK / ˈopən /

A1
  • adjecitve
  • Available for use; accessible
  • Not being hidden; available for others to see
  • Being available for customers to enter or use
  • Allowing everyone to use or take part in
  • Not secret anymore
  • Not closed or shut
  • Willing to accept new ideas and thoughts
  • noun
  • Name for a tennis or golf competition
  • verb
  • To make accessible or able to be used, e.g. road
  • To start the activities or services of a business
  • To make a space or hole appear in something
  • To move or change so that it is no longer closed
  • To start something, e.g. a new business

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

verify

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US / 'verɪfaɪ /

UK / ˈvɛrəˌfaɪ /

B2
  • verb
  • To prove that something is right, accurate or true

may

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US / meɪ /

UK / me /

A1
  • noun
  • 5th month of the year
  • other
  • Used to express a desire
  • Expresses permission, possibility or probability
  • Used to show that a thing could be true

less

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US / les /

UK / lɛs /

A1
  • adjecitve
  • Smaller in amount or degree
  • adverb
  • To a smaller degree
  • noun
  • A smaller amount
  • preposition
  • With the subtraction of

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

describe

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US / dɪ'skraɪb /

UK / dɪˈskraɪb /

A1
  • verb
  • To tell the appearance, sound, smell of something

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

superscript

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US / ˈsuːpəskrɪpt /

UK / ˈsuːpərskrɪpt /

C2
  • noun
  • In printing, a character placed higher than others

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

weird

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US / wɪəd /

UK / wɪrd /

B1
  • adjecitve
  • Odd or unusual; surprising; strange

imagine

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US / ɪ'mædʒɪn /

UK / ɪˈmædʒɪn /

A1
  • verb
  • To think creatively about; form mental picture of

probably

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US / ˈprɒbəbli /

UK / ˈprɑbəbli /

A1
  • adverb
  • That is likely to happen or be true

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

while

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US / waɪl /

UK / hwaɪl, waɪl /

A1
  • conjunction
  • In spite of the fact that; although
  • During the time that; at the same time
  • noun
  • Short amount of time

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

consider

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US / kən'sɪdə(r) /

UK / kənˈsɪdər /

A1
  • verb
  • To think carefully about something

khan

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US / kɑ:n /

UK / kɑn, kæn /

A1
  • other
  • A title given to rulers or other important people in Asian countries

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

whenever

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US / wenˈevə(r) /

UK / hwɛnˈɛvɚ /

A1
  • adverb
  • At any or every time that

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

recommend

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US / ˌrekə'mend /

UK / ˌrɛkəˈmɛnd /

A2
  • verb
  • To advise or suggest that someone do something

practice

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US / 'præktɪs /

UK / ˈpræktɪs /

A2
  • noun
  • The office and place for legal or medical work
  • Doing something many times to become better at it
  • verb
  • To work as a doctor or lawyer
  • To live according to the teachings of a religion
  • To do something many times to improve a skill

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

interesting

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US / ˈɪntrəstɪŋ /

UK / ˈɪntrɪstɪŋ, -tərɪstɪŋ, -təˌrɛstɪŋ /

A1
  • adjecitve
  • Taking your attention; making you want to know
  • verb
  • To make someone want to know about something
  • To persuade to do, become involved with something

include

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US / ɪnˈklu:d /

UK / ɪnˈklud /

A1
  • verb
  • To make someone, something part of a group

least

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US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

notation

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US / nəʊ'teɪʃn /

UK / noˈteʃən /

C2
  • noun
  • Set of written signs are used in music or math

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

watch

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US / wɒtʃ /

UK / wɑtʃ /

A1
  • noun
  • Period of time someone is responsible for guarding
  • Device you wear on your wrist that shows the time
  • Official warning statement, e.g. of bad weather
  • verb
  • To keep in check, manage, or control something
  • To look at something for entertainment, e.g. TV
  • To guard a place or people; protect child, etc.
  • To look at carefully to work out what is happening
  • To protect and care for someone or something

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

care

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US / keə(r) /

UK / kɛr /

A1
  • noun
  • Treatment you receive for your health or safety
  • Something that a person worries about
  • verb
  • To feel interest, concern, or worry
  • To look after someone or something

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

quadratic

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US / kwɒˈdrætɪk /

UK / kwɑˈdrætɪk /

A1
  • adjecitve
  • Polynomial of the second degree

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

essentially

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US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

great

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US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

choice

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US / tʃɔɪs /

UK / tʃɔɪs /

A1
  • adjecitve
  • Of good quality or taste; desirable
  • noun
  • Decision between two or more possibilities

draw

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US / drɔ: /

UK / drɔ /

A1
  • noun
  • Something that attracts people to visit a place
  • A lottery or prize
  • Result of a game, contest where the score is equal
  • verb
  • To attract attention to someone or something
  • To get closer to or approach something or someone
  • To influence a person's involvement in something
  • To move an object by pulling
  • To create an image using pen or pencil and paper
  • To take one thing out of a container, etc.
  • (Of 2 teams) to finish a game with the same score

focus

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US / 'fəʊkəs /

UK / ˈfokəs /

A2
  • noun
  • Main purpose or center of interest or activity
  • verb
  • To see clearly by adjusting your eyes or a camera
  • To keep your attention, concentration on one thing

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

academy

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US / ə'kædəmɪ /

UK / əˈkædəmi /

A2
  • noun
  • School that specializes in certain subjects

hand

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US / hænd /

UK / hænd /

A1
  • noun
  • Cards given to a player in a card game
  • Piece of a clock that points to the time
  • Someone who performs physical tasks or work
  • Body part at the end of a person's arm
  • Help for someone performing a particular action
  • Condition of having power or influence
  • Member of the crew of a ship
  • verb
  • To give something to someone personally

sine

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US / saɪn /

UK / saɪn /

C1
  • noun
  • Angle's ratio of side opposite hypotenuse

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

directionality

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US / dɪˌrekʃə'nælɪtɪ /

UK / dəˌrekʃə'nælətɪ /

A1
  • other
  • The property of being directional or maintaining a direction

notice

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US / 'nəʊtɪs /

UK / ˈnotɪs /

A1
  • noun
  • Time by when you must leave, e.g. if you are fired
  • Paper with an announcement, e.g. pinned to a board
  • verb
  • To become aware by sight, touch, or hearing

remember

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US / rɪ'membə(r) /

UK / rɪˈmɛmbɚ /

A1
  • verb
  • To give someone a gift, e.g. birthday, wedding
  • To hold a thought in your mind to not forget it
  • To bring a previous image or idea to your mind

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

without

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US / wɪˈðaʊt /

UK / wɪðˈaʊt, wɪθ- /

A1
  • preposition
  • Not with; not having

line

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US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

infinity

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US / ɪn'fɪnətɪ /

UK / ɪnˈfɪnɪti /

B2
  • noun
  • State of being without end; endless time, space

define

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US / dɪ'faɪn /

UK / dɪˈfaɪn /

A2
  • verb
  • To explain the meaning of words
  • To set or mark the limits of something

pop

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US / pɒp /

UK / pɑp /

B2
  • adjecitve
  • Type of music or art popular with many people
  • noun
  • Sweet soda drink
  • verb
  • To cause something to open or burst suddenly
  • To go to or in a place for a brief period of time

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

numerator

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US / ˈnju:məreɪtə(r) /

UK / ˈnu:məreɪtə(r) /

C2
  • noun
  • Dividend of a fraction

pause

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US / pɔ:z /

UK / pɔz /

A2
  • noun
  • A temporary break before continuing
  • Function on a device to stop and restart it
  • Sign to hold a musical note a bit longer
  • verb
  • To stop doing for a while before continuing

correct

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US / kə'rekt /

UK / kəˈrɛkt /

A2
  • adjecitve
  • Being suitable and appropriate for an occasion
  • True or accurate
  • verb
  • To fix a problem
  • To write marks on a piece of work to show mistakes
  • To punish in order to improve

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

become

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US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

deal

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US / di:l /

UK / dil /

A1
  • verb
  • To cope with something - usually troubles
  • To give (something bad e.g. news) to
  • To buy and sell illegal drugs
  • To give out (cards, etc.) to; distribute
  • To do business with someone or to sell products

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

sense

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US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

behaviour

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US / bɪˈheɪvjə(r) /

UK / bɪˈhevjɚ /

A1
  • noun
  • The way a person or thing acts; manner

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

address

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US / ə'dres /

UK / əˈdrɛs /

A1
  • noun
  • Exact street location of a place
  • A formal speech to a group of people
  • verb
  • To write the place someone lives on a letter
  • To refer to someone or something formally
  • To make a formal speech to a group of people
  • To try to find a solution to; think about

sum

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US / sʌm /

UK / sʌm /

A2
  • noun
  • Amount when all is added together; total
  • verb
  • To add two or more numbers together; total

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

zero

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US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

scale

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US / skeɪl /

UK / skel /

A2
  • noun
  • Size, level, or amount when compared
  • Small hard plates that cover the body of fish
  • Device that is used to weigh a person or thing
  • Range of numbers from the lowest to the highest
  • Dimensions or size of something
  • verb
  • To change the size of but keep the proportions
  • To climb something large (e.g. a mountain)
  • To remove the scales of a fish

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

particular

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US / pəˈtɪkjələ(r) /

UK / pɚˈtɪkjəlɚ, pəˈtɪk- /

B2
  • adjecitve
  • One specific (one)
  • Having firm ideas about what is desirable
  • Being special or more than is typical

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

asymptote

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US / 'æsɪmptəʊt /

UK / 'æsɪmˌtoʊt /

A1
  • noun
  • Straight line that is the limiting value of a curve; can be considered as tangent at infinity

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

familiar

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US / fəˈmɪliə(r) /

UK / fəˈmɪljɚ /

A2
  • adjecitve
  • Well-known or easily recognized

accurate

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US / ˈækjərət /

UK / ˈækjərɪt /

A2
  • adjecitve
  • With no mistake or error; Correct

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

large

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US / lɑ:dʒ /

UK / lɑ:rdʒ /

A1
  • adjecitve
  • Big; of great size; broad, tall, wide, or fat

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

incorrect

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US / ˌɪnkəˈrekt /

UK / ˌɪnkəˈrɛkt /

B1
  • adjecitve
  • Being wrong or inaccurate

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

far

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US / fɑ:(r) /

UK / fɑr /

A1
  • adjecitve
  • A long way away
  • Being a long way away
  • adverb
  • To a large degree or extent

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

confusing

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US / kənˈfju:zɪŋ /

UK / kənˈfjuzɪŋ /

A2
  • adjecitve
  • Being hard to understand
  • verb
  • To make something unclear or hard to understand

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

change

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US / tʃeɪndʒ /

UK / tʃendʒ /

A1
  • noun
  • Exchange of one set of clothes for another
  • Money in the form of coins instead of paper
  • Money returned after giving too much
  • Act of making or becoming something else
  • verb
  • To exchange one set of clothes for another
  • To exchange one kind of money for another
  • To replace something with another thing
  • To make or become something else
  • To go from one train, bus, etc. and go to another

approach

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US / ə'prəʊtʃ /

UK / əˈprəʊtʃ /

A2
  • noun
  • Means of reaching a place, often a road or path
  • Request of someone with a specific goal in mind
  • Specific way to handle a project, task, problem
  • verb
  • To get close to reaching something or somewhere
  • To request someone to do something specific

encourage

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US / ɪn'kʌrɪdʒ /

UK / ɛnˈkɚrɪdʒ, -ˈkʌr- /

A2
  • verb
  • To increase the chance of something happening
  • To make someone more determined or confident

top

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US / tɒp /

UK / tɑp /

A1
  • adjecitve
  • Being good or great; excellent
  • Being the most in degree or quality
  • noun
  • Item of clothing covering shoulders to waist, hips
  • A cover or lid
  • Part (e.g. road) that is the furthest away
  • Highest or upper part or point of something
  • Best or highest status or position
  • Flat upper surface or edge of an object
  • Child's toy that spins on its point
  • Upper section or leaves of fruits and vegetables
  • Winning in a sport or contest
  • verb
  • To be higher or larger than a specific value
  • To arrive at the highest point of something
  • To put a cover or layer or over something
  • To kill; murder
  • To hold the highest position on a list
  • To be more important, successful or better than
  • To beat someone or win at a game

direction

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US / də'rekʃn /

UK / dɪˈrɛkʃən, daɪ- /

A2
  • noun
  • When someone tells people what to do
  • Describes the way you are going, e.g. North

pay

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US / peɪ /

UK / pe /

A1
  • noun
  • Money you receive from your job, work, etc.
  • verb
  • To give money for goods or work done
  • To give (attention, respect, etc.) to
  • To be punished or suffer for something you did
  • To make (a visit) to a person or place

pretty

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US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

between

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US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

attention

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US / əˈtenʃn /

UK / əˈtɛnʃən /

A2
  • noun
  • Taking notice of someone or something
  • (Soldiers) Standing with straight backs
  • Subtitles section
  • We're asked to describe the behavior of the function q around its vertical asymptote at x equals negative three.
  • And like always, if you're familiar with this, I encourage you to pause it and see if you can get some practice, and if you're not, well, I'm about to do it with you.
  • All right, so this is q of x.
  • It's defined by a rational expression.
  • Whenever I'm dealing with asymptotes, I like to factor the numerators and the denominators so I can make more sense of things.
  • So the numerator here, what two numbers, if their product is two and their sum is three, well, that's two and one.
  • So I can factor this as x plus one times x plus two.
  • If that's unfamiliar to you, I recommend you watch the videos on Khan Academy on factoring quadratics.
  • And over x plus three.
  • And when x equals negative one or x equals negative two, it would make the numerator equal zero without making the denominator equal zero.
  • So those are points where the function's equal to zero.
  • But when x equals negative three, the denominator equals zero while the numerator is not equal to zero.
  • So we're dividing by zero.
  • And so that's a pretty good sign of a vertical asymptote.
  • That our function as we approach that value is either gonna pop up like that or it's going to pop down like that.
  • Or maybe, or either way.
  • It could pop up like that or it could go down something like that.
  • But we're gonna have a vertical asymptote.
  • That the function as you approach x equals negative three, that the function is going to approach either positive infinity or negative infinity or it might do positive infinity from one direction or negative infinity from another direction.
  • And if this idea of directionality is a little bit confusing, well that's what we're about to address in this video.
  • So let me just draw a number line here that focuses on these interesting values.
  • So we care about x equals negative three.
  • And then the other interesting values may be negative two, negative one.
  • It's all there.
  • Now what does it mean to be approaching x?
  • What does it mean for x to be approaching negative three from the negative direction?
  • And just to be clear, this little superscript right over here, that means we're approaching from the negative direction.
  • So that means we're approaching from values more negative than negative three.
  • So those are these values right over here.
  • We are approaching from that direction.
  • Another way to think about it is we approach from the negative direction.
  • We're on the interval x is less than negative three.
  • So let's think about what the sine of q of x is going to be as we're approaching negative three from that negative direction, from the left.
  • Well, if we have something less than negative three and you add one, this is going to be negative.
  • If you have something less than negative three and you add two, that's going to be negative as well.
  • And if you have something less than negative three and you add three, well, that's going to be negative as well.
  • So negative times a negative is a positive but then you divide by a negative.
  • It's going to be a negative.
  • So q of x is going to be negative on that interval.
  • We have our vertical asymptote.
  • We approach negative three from the left-hand side.
  • Well, q of x is going to be negative and so it's going to approach negative infinity.
  • So as x approaches negative three from the negative direction, q of x is going to approach negative infinity.
  • So, at least this is accurate.
  • This is accurate, and this is accurate right over here.
  • And you can validate that.
  • Try some values out.
  • Try negative, let's see, if you did negative three point, you know, q of, q of negative three point, negative three point one.
  • Once again, that's on the left side.
  • It might be like right over there.
  • Actually, it'd probably be a little bit further.
  • It might be something like this, like the scale that I've drawn it on.
  • Q of negative three point one, if you want to verify it, it's gonna be negative three point one plus one, which is negative two point one, times negative three point one plus two, which is negative, negative one point one,
  • One point one, I could put that in parentheses just to make it clear.
  • And then all of that is going to be over, well, negative three point one plus three is going to be, is going to be negative zero point one.
  • So, notice, whatever we get up here, this positive value, we're essentially going to, if we're dividing it by negative zero point one, that's like multiplying it by negative 10. So, it's gonna get, it's gonna become a very negative value.
  • And if instead of it being negative three point one, imagine if it was negative three point zero one.
  • And this would be a zero one here.
  • This would be a zero one here.
  • And this would be a zero one here.
  • And so, this denominator, you're dividing by negative zero point zero one, it's gonna be an even larger negative value.
  • So, you're gonna approach negative infinity.
  • So, it's gonna be one of these two choices.
  • Now, let's think about what happens as we approach x from the positive direction.
  • And that's what, that's what this notation over there means, this superscript on the right hand side, the positive direction.
  • So, we're going to approach x from the positive direction.
  • And I'm gonna pay attention, in particular, to the interval between negative two and negative three, because then we know we don't have any weird sign changes going on in the numerator.
  • So, I care about the interval negative three is less than x, which is less than negative two.
  • So, I can draw an open circle here, say we're not considering when we're at negative two.
  • And of course, we're not going to include negative three, because our function isn't defined there.
  • But over this interval, so, x plus one is still going to be negative.
  • X plus one is still going to be negative.
  • If you took a negative 2.5 plus one, it's going to be negative 1.5. X plus two is still going to be negative.
  • You're taking values that are more negative than negative two, that are less than negative two.
  • So, you add two to that, you're still going to be negative.
  • And then, let's see, if you add three, if you add three to these values, remember, they're greater than negative three.
  • Or you could say they are less negative than negative three.
  • Well, then, this is going to give you a positive value.
  • This is going to give you a positive value.
  • And think about it.
  • Q of, I don't know, negative 2.99.
  • What is that going to be equal to?
  • If you add one to that, that is negative 1.99.
  • And if you add two to that, times negative 0.99, all of that over, negative 2.99 plus three, well, that's going to be 0.01.
  • So, you're going to get a positive value on top.
  • And then, you're going to divide it by 0.01.
  • That's the same thing as multiplying by 100.
  • So, you're going to get larger and larger values.
  • You're going to approach infinity as you get closer and closer to it from the right-hand side.
  • So, Q of X is going to approach positive infinity.
  • So, this is the choice that is correct.
  • This one is wrong.
  • This says we're going to approach negative infinity.
  • So, that's incorrect.
  • And we will go with that choice.