Linear or Nonlinear?

Question 1

The inputs in the table rise by 2 from row to row. Is the function the table shows linear?

Accepted Answer

No, because y climbs by 4, then by 8, then by 12 across those equal steps

Answer

No, because no output is a multiple of its input

Answer

Yes, because y rises by 2 for each 1 that x rises

Answer

Yes, because both columns rise from row to row

Question 2

How would you describe the function that is graphed on the plane?

Accepted Answer

It is a function, but its rate of change is not constant

Answer

It is a linear function, because its graph is a straight line

Answer

It is not a function, because one input is assigned two outputs

Answer

It is a linear function, because its graph has no break in it

Question 3

The inputs in the table rise by 1 from row to row. Is the function the table shows linear?

Accepted Answer

No, because equal steps in x do not give equal steps in y

Answer

No, because the table does not include the input 0

Answer

Yes, because y grows every time x grows

Answer

Yes, because each input is assigned exactly one output

Question 4

How would you describe the function that is graphed on the plane?

Accepted Answer

It is a linear function, and its rate of change is the same everywhere

Answer

It is a function, but its rate of change keeps changing

Answer

It is not a function, because one input is assigned two outputs

Answer

It is not linear, because its graph does not reach the origin

Question 5

Each row of the table steps the input on by 1. What does the output do across those steps?

Accepted Answer

It changes by a different amount each time, so the function is not linear

Answer

It changes by the same amount each time, so the function is linear

Answer

It changes by a different amount each time, and the function is still linear

Answer

It stays at the value it started from, so the function is linear

Question 6

The rule y = 5x - 3 pairs each input x with an output y. Does the rule define a linear function?

Accepted Answer

Yes, because it multiplies x by a fixed number and adds a constant

Answer

No, because y changes by 5 rather than by 1 for each step in x

Answer

Yes, because each input is paired with exactly one output

Answer

No, because the pairing leaves some inputs with no output

Question 7

Would the graph of y = 5x - 2 be a straight line?

Accepted Answer

Yes, because the rule has the form y = mx + b

Answer

No, because the graph would bend where x is negative

Answer

No, because a straight line has to pass through the origin

Answer

Yes, because every input is paired with exactly one output

Question 8

The inputs in the table rise by 1 from row to row. Is the function the table shows linear?

Accepted Answer

Yes, because equal steps in x give equal steps in y

Answer

No, because equal steps in x do not give equal steps in y

Answer

No, because the table does not include the input 0

Answer

Yes, because each input is assigned exactly one output

Question 9

Each row of the table steps the input on by 1. What does the output do across those steps?

Accepted Answer

It changes by the same amount each time, so the function is linear

Answer

It changes by a different amount each time, so the function is not linear

Answer

It changes by the same amount each time, and the function is still not linear

Answer

It doubles from one row to the next, so the function is not linear

Question 10

A function is given by the rule y = 2x^2. Is that function linear?

Accepted Answer

No, because its rate of change is not constant

Answer

No, because it has no y-intercept

Answer

Yes, because each input is assigned exactly one output

Answer

Yes, because the constant 0 is its starting value

Question 11

The rule y = 2^x pairs each input x with an output y. Does the rule define a linear function?

Accepted Answer

No, because it builds y by using the input as an exponent, so equal steps in x give unequal steps in y

Answer

Yes, because it multiplies x by a fixed number and adds a constant

Answer

Yes, because each input is paired with exactly one output

Answer

No, because the pairing leaves some inputs with no output

Question 12

Does the graph drawn on the plane keep the same rate of change all the way along it?

Accepted Answer

No, because its steepness keeps changing, so the function is not linear

Answer

Yes, because its steepness never changes, so the function is linear

Answer

Yes, because the graph is drawn in one unbroken piece

Answer

No, because the graph does not pass through the origin

Question 13

A ball is dropped and the distance it has fallen after t seconds is 5 multiplied by t multiplied by t. Is the distance fallen a linear function of the time?

Accepted Answer

No, because the distance added each second keeps growing rather than staying the same

Answer

No, because the ball eventually hits the ground

Answer

Yes, because each time gives exactly one distance

Answer

Yes, because the distance rises every second

Question 14

How would you describe the function that is graphed on the plane?

Accepted Answer

It is a function, but its rate of change is not constant

Answer

It is a linear function, because its graph is a straight line

Answer

It is not a function, because one input is assigned two outputs

Answer

It is a linear function, because its graph has no break in it

Question 15

A function is given by the rule y = -2x - 7. Is that function linear?

Accepted Answer

Yes, because its rate of change is constant

Answer

No, because its rate of change is not constant

Answer

No, because it does not pass through the origin

Answer

Yes, because each input is assigned exactly one output

Question 16

The rule y = x^2 + 4 pairs each input x with an output y. Does the rule define a linear function?

Accepted Answer

No, because it builds y by squaring the input, so equal steps in x give unequal steps in y

Answer

Yes, because it multiplies x by a fixed number and adds a constant

Answer

Yes, because each input is paired with exactly one output

Answer

No, because the pairing leaves some inputs with no output

Question 17

Each row of the table steps the input on by 1. What does the output do across those steps?

Accepted Answer

It changes by the same amount each time, so the function is linear

Answer

It changes by a different amount each time, so the function is not linear

Answer

It changes by the same amount each time, and the function is still not linear

Answer

It doubles from one row to the next, so the function is not linear

Question 18

The rule y = -3x - 9 pairs each input x with an output y. Does the rule define a linear function?

Accepted Answer

Yes, because it multiplies x by a fixed number and adds a constant

Answer

No, because y changes by 3 rather than by 1 for each step in x

Answer

Yes, because each input is paired with exactly one output

Answer

No, because the pairing leaves some inputs with no output

Question 19

Does the graph drawn on the plane keep the same rate of change all the way along it?

Accepted Answer

No, because its steepness keeps changing, so the function is not linear

Answer

Yes, because its steepness never changes, so the function is linear

Answer

Yes, because the graph is drawn in one unbroken piece

Answer

No, because the graph does not pass through the origin

Question 20

The inputs in the table rise by 1 from row to row. Is the function the table shows linear?

Accepted Answer

Yes, because equal steps in x give equal steps in y

Answer

No, because equal steps in x do not give equal steps in y

Answer

No, because the table does not include the input 0

Answer

Yes, because each input is assigned exactly one output

Question 21

The inputs in the table rise by 4 from row to row. Is the function the table shows linear?

Accepted Answer

No, because y climbs by 5, then by 9, then by 13 across those equal steps

Answer

No, because no output is a multiple of its input

Answer

Yes, because y rises by 1.25 for each 1 that x rises

Answer

Yes, because both columns rise from row to row

Question 22

Does the graph drawn on the plane keep the same rate of change all the way along it?

Accepted Answer

Yes, because its steepness never changes, so the function is linear

Answer

No, because its steepness keeps changing, so the function is not linear

Answer

No, because the graph is steeper on its right-hand side

Answer

Yes, because each input on it is assigned exactly one output

Question 23

A gym charges a $25 joining fee and then $18 for each month of membership. Is the total paid a linear function of the months of membership?

Accepted Answer

Yes, because the total rises by the same $18 for every extra month

Answer

Yes, because the total paid is proportional to the months of membership

Answer

No, because the $25 is paid only at the start

Answer

No, because the total is never $0

Question 24

The inputs in the table rise by 2 from row to row. Is the function the table shows linear?

Accepted Answer

Yes, because y changes by the same 4 across every one of those equal steps

Answer

No, because the x-values do not rise by 1 from row to row

Answer

No, because the table does not include the input 0

Answer

Yes, because each input is assigned exactly one output

Question 25

Would the graph of y = x^3 be a straight line?

Accepted Answer

No, because the steps in y keep growing while the steps in x stay equal

Answer

Yes, because the rule has the form y = mx + b

Answer

Yes, because every input is paired with exactly one output

Answer

No, because the rule has no y-intercept

Question 26

Does the graph drawn on the plane keep the same rate of change all the way along it?

Accepted Answer

Yes, because its steepness never changes, so the function is linear

Answer

No, because its steepness keeps changing, so the function is not linear

Answer

No, because the graph is steeper on its right-hand side

Answer

Yes, because each input on it is assigned exactly one output

Question 27

The graph shown holds every point of a function. Is the function linear?

Accepted Answer

Yes, because the graph is a straight line, so equal steps in x give equal steps in y

Answer

No, because the graph does not pass through the origin

Answer

No, because the rate of change of the graph is not constant

Answer

Yes, because each input is assigned exactly one output

Question 28

Each row of the table steps the input on by 1. What does the output do across those steps?

Accepted Answer

It changes by a different amount each time, so the function is not linear

Answer

It changes by the same amount each time, so the function is linear

Answer

It changes by a different amount each time, and the function is still linear

Answer

It stays at the value it started from, so the function is linear

Question 29

How would you describe the function that is graphed on the plane?

Accepted Answer

It is a linear function, and its rate of change is the same everywhere

Answer

It is a function, but its rate of change keeps changing

Answer

It is not a function, because one input is assigned two outputs

Answer

It is not linear, because its graph does not reach the origin

Question 30

The graph shown holds every point of a function. Is the function linear?

Accepted Answer

No, because the graph is not a straight line

Answer

No, because the graph does not pass through the origin

Answer

Yes, because each input is assigned exactly one output

Answer

Yes, because the graph is a single unbroken curve

Question 31

A colony of bacteria doubles in number every hour. Is the number of bacteria a linear function of the hours passed?

Accepted Answer

No, because the number added each hour keeps growing rather than staying the same

Answer

No, because the colony cannot hold a fraction of a bacterium

Answer

Yes, because each hour gives exactly one number of bacteria

Answer

Yes, because the number rises every hour without stopping

Question 32

Would every point in the table lie on one straight line if they were plotted?

Accepted Answer

Yes, because the outputs change by a fixed amount

Answer

No, because a straight line would have to pass through the origin

Answer

No, because the outputs do not change by a fixed amount

Answer

Yes, because the four rows are listed in order of their inputs

Question 33

Would every point in the table lie on one straight line if they were plotted?

Accepted Answer

No, because the outputs do not change by a fixed amount

Answer

Yes, because a straight line can be drawn through any four points

Answer

Yes, because the outputs change every time the inputs do

Answer

No, because the table does not include the input 0

Question 34

A water tank starts with 40 liters and loses 5 liters every hour. Is the volume left a linear function of the hours passed?

Accepted Answer

Yes, because the volume falls by the same 5 liters every hour

Answer

Yes, because the volume is proportional to the hours passed

Answer

No, because the volume is falling rather than rising

Answer

No, because the tank starts at 40 rather than at 0

Question 35

The inputs in the table rise by 3 from row to row. Is the function the table shows linear?

Accepted Answer

Yes, because y changes by the same 9 across every one of those equal steps

Answer

No, because the x-values do not rise by 1 from row to row

Answer

No, because the table does not include the input 0

Answer

Yes, because each input is assigned exactly one output

Question 36

The graph shown holds every point of a function. Is the function linear?

Accepted Answer

No, because the graph is not a straight line

Answer

No, because the graph does not pass through the origin

Answer

Yes, because each input is assigned exactly one output

Answer

Yes, because the graph is a single unbroken curve

Question 37

A function is given by the rule y = x + 9. Is that function linear?

Accepted Answer

Yes, because its rate of change is constant

Answer

No, because its rate of change is not constant

Answer

No, because it does not pass through the origin

Answer

Yes, because each input is assigned exactly one output

Question 38

A function is given by the rule y = x^3 + 2. Is that function linear?

Accepted Answer

No, because its rate of change is not constant

Answer

No, because it has no y-intercept

Answer

Yes, because each input is assigned exactly one output

Answer

Yes, because the constant 2 is its starting value

Question 39

The inputs in the table rise by 1 from row to row. Is the function the table shows linear?

Accepted Answer

No, because equal steps in x do not give equal steps in y

Answer

No, because the table does not include the input 0

Answer

Yes, because y grows every time x grows

Answer

Yes, because each input is assigned exactly one output

Question 40

The graph shown holds every point of a function. Is the function linear?

Accepted Answer

Yes, because the graph is a straight line, so equal steps in x give equal steps in y

Answer

No, because the graph does not pass through the origin

Answer

No, because the rate of change of the graph is not constant

Answer

Yes, because each input is assigned exactly one output

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Linear or Nonlinear?

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Board Games: Teacher-led, projected to the class

Like what you see?

Bug Blast

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Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner

Linear or Nonlinear?

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner