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Interpreting features of functions (example 2) | Algebra II | Khan Academy

Video vocabulary

you

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US / jʊ /

UK / ju /

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

thickness

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US / ˈθɪknəs /

UK / ˈθɪknɪs /

A2
  • noun
  • Distance between the opposite edges of a thing

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

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

answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

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

than

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US / ðən /

UK / ðən /

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

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

fair

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US / feə(r) /

UK / fɛr /

A1
  • adjecitve
  • Neither very good nor very bad; average
  • (Of skin) light colored; not dark
  • Quite good; quite a lot
  • Treating all people the same way
  • (Of hair) light colored; blonde
  • (Of weather) sunny; not raining
  • noun
  • Event for companies to show their products
  • Event to sell things to help a charity

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

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

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

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

magnitude

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US / ˈmægnɪtju:d /

UK / ˈmæɡnɪˌtud, -ˌtjud /

B2
  • noun
  • Number representing force of an earthquake
  • Size or importance
  • Number representing the brightness of a star

below

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US / bɪ'ləʊ /

UK / bɪˈlo /

A1
  • preposition
  • In a lower position, place, or level

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

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

seven

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US / ˈsevn /

UK / ˈsɛvən /

A1
  • number
  • Number 7

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

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

same

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US / seɪm /

UK / sem /

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

scrape

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US / skreɪp /

UK / skrep /

B1
  • noun
  • Bad or unpleasant incident
  • other
  • To move roughly across the surface of something
  • verb
  • To take something off a surface with a sharp tool
  • To damage the surface by moving something roughly
  • To remove something by roughly brushing it off

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

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

whether

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US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

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

effect

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US / ɪ'fekt /

UK / ɪˈfɛkt /

A1
  • noun
  • An advantage, benefit
  • Change brought about by a cause; result

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

but

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US / bət /

UK / bʌt,bət /

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

amount

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US / ə'maʊnt /

UK / əˈmaʊnt /

A1
  • noun
  • Quantity of something
  • verb
  • To add up to a certain figure

statement

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US / ˈsteɪtmənt /

UK / ˈstetmənt /

A2
  • noun
  • Record of activity in a bank account over time
  • Act or process of saying something formally

standard

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US / 'stændəd /

UK / ˈstændəd /

A2
  • adjecitve
  • Being the accepted normal level of quality
  • (Of a language) being the most accepted in a place
  • noun
  • Official unit of measuring something
  • Principle of behaving in a moral way

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

fact

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US / fækt /

UK / fækt /

A1
  • noun
  • Something that is known or proved to be true

for

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US / fə(r) /

UK / fɔr,fə /

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

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

piece

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US / pi:s /

UK / pis /

A1
  • noun
  • A counter in a board game
  • Small part of something larger
  • verb
  • To put items together to assemble something

lower

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US / 'ləʊə(r) /

UK / ˈlaʊɚ, laʊr /

A2
  • adjecitve
  • In a position more near the bottom
  • verb
  • To move something downward to the ground

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)

per

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US / pə(r) /

UK / pɚ /

A2
  • preposition
  • In the manner directed or suggested
  • For each; during each

velocity

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US / və'lɒsətɪ /

UK / vəˈlɑsɪti /

B1
  • noun
  • Speed in a given direction

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

speed

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US / spi:d /

UK / spid /

A2
  • noun
  • How fast or slow something is or is done
  • verb
  • To move quickly when completing an action
  • To drive a vehicle faster than laws allow

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

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

move

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US / mu:v /

UK / muv /

A1
  • noun
  • Act of moving a playing piece in chess, etc.
  • An action; doing something
  • Step taken to achieve a goal
  • verb
  • To cause someone to have certain emotions
  • To cause something to change to a different place
  • To change where people live or a business operates
  • To take action to do or achieve something

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

they

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US / ðeɪ /

UK / ðe /

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

show

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US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

sandpaper

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US / 'sændpeɪpə(r) /

UK / ˈsændˌpepɚ /

C2
  • noun
  • Paper with glued sand used for smoothing wood

fast

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US / fɑ:st /

UK / fæst /

A1
  • adjecitve
  • In a way that is difficult to move or change
  • Moving or able to move quickly
  • Showing time that is later than the actual time
  • adverb
  • With a great deal of speed
  • noun
  • Period of time when a person chooses not to eat
  • verb
  • To refuse food for a long time

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

close

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US / kləʊz /

UK / kloʊz /

A1
  • adjecitve
  • Almost; near
  • (Of a friend) well-known; liked by others
  • Being near or related
  • Similar; nearly the same
  • verb
  • To come progressively nearer to something
  • To end; to bring to an end
  • To make something shut; stop from being open

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

evenness

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US / ˈiːvənnəs /

UK / ˈiːvənnəs /

B2
  • noun
  • A quality of uniformity and lack of variation

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

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

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

thick

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US / θɪk /

UK / θɪk /

A2
  • adjecitve
  • Difficult to see through, as fog
  • Full of (people, etc.)
  • (Of a liquid) that moves or pours slowly
  • Stupid; not smart
  • (Of person's accent) hard to understand
  • Having a large distance between two surfaces

here

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US / hɪə(r) /

UK / hɪr /

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

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

convention

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US / kənˈvenʃn /

UK / kənˈvɛnʃən /

A2
  • adjecitve
  • Concerning a large formal assembly or meeting
  • noun
  • Official agreement between two or more countries
  • Large formal assembly, e.g. to make laws
  • Proper and widely accepted way of behaving

millimetre

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US / ˈmɪlimi:tə(r) /

UK / ˈmɪlimiːtər /

B1
  • noun
  • Unit of measure, 1/1000 of a metre (symbol mm)

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

matter

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US / 'mætə(r) /

UK / ˈmætɚ /

A1
  • noun
  • Material all things are made of that fills space
  • Problem or reason for concern
  • verb
  • To be of great importance; to count

keep

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US / ki:p /

UK / kip /

A1
  • noun
  • Large, strong tower in the middle of a castle
  • Money spent on you so you can live in a place
  • verb
  • To continue doing something; not to stop
  • To stop balls going in a goal in sports
  • To not give back or return something
  • (Of food) to not spoil or not rot
  • To take possession of something to own, e.g. a pet
  • To have and continue to hold something
  • To do something that you have promised or agreed
  • To stay in a certain place or condition
  • To maintain the rules

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

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

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

from

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US / frəm /

UK / frʌm, frɑm,frəm /

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

hey

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US / heɪ /

UK / he /

A1
  • exclamation
  • What you say when you want someone's attention

large

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US / lɑ:dʒ /

UK / lɑ:rdʒ /

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

early

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US / ˈɜ:li /

UK / ˈɜ:rli /

A1
  • adjecitve
  • Happening or appearing before
  • adverb
  • Coming/happening before others in a time sequence
  • Happening sooner than expected

experiment

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US / ɪk'sperɪmənt /

UK / ɪkˈspɛrəmənt /

A2
  • noun
  • Test performed to assess new ideas or theories
  • verb
  • To create and perform tests to research something
  • To try something new that you haven't tried before

any

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US / 'enɪ /

UK / ˈɛni /

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

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

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

enough

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US / ɪˈnʌf /

UK / ɪˈnʌf /

A1
  • adjecitve
  • Sufficient to answer the need
  • adverb
  • To a satisfactory degree
  • pronoun
  • Equal to what is needed; as much as required
  • Adequate number or amount

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

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

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

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’

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

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

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

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

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

absolute

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US / ˈæbsəlu:t /

UK / ˈæbsəˌlut /

A2
  • adjecitve
  • Complete; total; pure; not limited in any way
  • noun
  • Something that is complete, total, pure, certain

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)

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

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

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

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon
  • verb
  • To agree to support a proposal at a meeting

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

wood

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US / wʊd /

UK / wʊd /

A2
  • adjecitve
  • Living or existing in the woods
  • Made from the material from trees
  • noun
  • Person's name
  • Land covered with trees, smaller than a forest
  • Cut tree used for making fires or building things
  • verb
  • To plant an area of land with trees

meter

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US / ˈmi:tə(r) /

UK / ˈmitɚ /

A1
  • noun
  • Unit of length equal to 100 cm or about 39 inches
  • Device for measuring things e.g. gas
  • Device to put money into to rent a parking place
  • Rhythm of a poem
  • verb
  • To measure water, etc. when it has to be paid for

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)

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

choice

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US / tʃɔɪs /

UK / tʃɔɪs /

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

with

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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

six

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US / sɪks /

UK / sɪks /

A1
  • number
  • 6

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

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

increase

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US / ɪn'kri:s /

UK / ɪnˈkris /

A1
  • noun
  • Fact of increasing; amount something grows by
  • verb
  • To make or become larger in size or amount
  • Subtitles section
  • Cid is experimenting with a piece of sandpaper and some wood.
  • He tries scraping the piece of sandpaper over the wood in different ways to see how much is scraped off.
  • The thickness of wood scraped off, in millimeters, as a function of the speed of the sandpaper, in meters per second.
  • t of v.
  • So this is the thickness scraped off.
  • So that's the thickness, or how much is scraped off.
  • And it is a function of speed.
  • One, they're using v and also they're getting negative value.
  • So we care about the direction.
  • It's actually the velocity.
  • So this is how much is scraped off as a function of velocity.
  • It's shown below.
  • And so if the velocity is greater than 0, that means that the sandpaper is moving to the right.
  • That makes sense.
  • That's the standard convention.
  • And if the velocity is less than 0, it means the sandpaper is moving to the left.
  • Fair enough.
  • The function is even.
  • What is the significance of the evenness of this function?
  • Well, the fact that it's even means that t of v is equal to t of negative v. So that tells us that if our velocity is 8 meters per second to the left we're going to get as much scraped off as if we go 8 millimeters per second to the right.
  • And we see that right over here.
  • So that is equal to that.
  • If we go at 6 meters per second to the left we're going to get just as much scraped off as we go 6 millimeters-- 6 meters per second, these are in meters per second-- to the right.
  • So these two are going to be the same.
  • So it's really telling us-- and we could say do it for 4 meters per second and negative 4-- is it doesn't matter if we go to the left or the right.
  • What really matters is the magnitude of the velocity or the absolute value of it.
  • But it doesn't matter if we're going to the left or the right.
  • Whether we're going to the left or the right for a given magnitude of velocity we are going to get the same amount scraped off.
  • Now let's see which of these choices are consistent with what I just said.
  • Moving the sandpaper faster scrapes off more wood.
  • Well, that's true.
  • We see as the speed increases, or the magnitude of the speed increases, we scrape off more wood.
  • As the magnitude of the speed, this negative 8, you might say, hey, that's lower than negative 2, but the magnitude is larger.
  • We're going 8 meters per second to the left and we're scraping off more.
  • So this is a true statement, but it's not the significance of the evenness of the function.
  • This could have been true even if this was a seven, but then this function would no longer be even.
  • The piece of wood is six millimeters thick.
  • We actually don't get any of that from the function.
  • Moving the sandpaper to the right has the same effect as moving it to the left.
  • Well, that seems pretty close to what I had said earlier.
  • That for a given speed to the right or to the left, we get the same amount that is taken off of the piece of sandpaper, or the piece of wood.
  • So this looks like our answer.
  • Keeping the sandpaper still doesn't scrape off any wood.
  • Well, that is true but once again is not the significance of the evenness of this function.