Writing a Transformed Function

Question 1

The graph of y = x^3 is shifted 5 units left and 6 units down. What is the equation of the image?

Accepted Answer

y = (x + 5)^3 - 6

Answer

y = (x - 5)^3 - 6

Answer

y = (x + 5)^3 + 6

Answer

y = (x + 6)^3 - 5

Question 2

The blue curve is y = x^2 and the purple curve is its image after a shift. What is the equation of the image?

Accepted Answer

y = (x - 4)^2 + 5

Answer

y = (x + 4)^2 + 5

Answer

y = (x - 4)^2 - 5

Answer

y = (x - 5)^2 + 4

Question 3

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = -4|x - 1| - 5

Answer

y = -4|x + 1| - 5

Answer

y = 4|x - 1| - 5

Answer

y = -|x - 1| - 5

Question 4

The point (3, 27) on the graph of y = x^3 moves to (3, 54) under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = 2x^3

Answer

y = (1/2)x^3

Answer

y = 4x^3

Answer

y = (1/4)x^3

Question 5

The graph of y = x^3 is reflected across the y-axis and shifted 6 units up. What is the equation of the image?

Accepted Answer

y = (-x)^3 + 6

Answer

y = (-x)^3 - 6

Answer

y = (x + 6)^3

Answer

y = -(-x)^3 + 6

Question 6

The graph of y = 3x is shifted 1 unit right and 6 units down. What is the equation of the image?

Accepted Answer

y = 3x - 1 - 6

Answer

y = 3x + 1 - 6

Answer

y = 3x - 1 + 6

Answer

y = 3x + 6 + 1

Question 7

The graph of y = x^2 is shifted 6 units right and 2 units up. What is the equation of the image?

Accepted Answer

y = (x - 6)^2 + 2

Answer

y = (x + 6)^2 + 2

Answer

y = (x - 6)^2 - 2

Answer

y = (x - 2)^2 + 6

Question 8

The graph of y = 3x is shifted 6 units right and 5 units up. What is the equation of the image?

Accepted Answer

y = 3x - 6 + 5

Answer

y = 3x + 6 + 5

Answer

y = 3x - 6 - 5

Answer

y = 3x - 5 + 6

Question 9

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = 3|x + 2| - 5

Answer

y = 3|x - 2| - 5

Answer

y = -3|x + 2| - 5

Answer

y = |x + 2| - 5

Question 10

The graph of y = 3x is reflected across the y-axis and shifted 8 units up. What is the equation of the image?

Accepted Answer

y = 3-x + 8

Answer

y = 3-x - 8

Answer

y = 3x + 8

Answer

y = -3-x + 8

Question 11

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = 2|x - 5| - 1

Answer

y = 2|x + 5| - 1

Answer

y = -2|x - 5| - 1

Answer

y = |x - 5| - 1

Question 12

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = 4|x - 1| + 5

Answer

y = 4|x + 1| + 5

Answer

y = -4|x - 1| + 5

Answer

y = |x - 1| + 5

Question 13

The graph of y = |x| is reflected across the x-axis and shifted 2 units down. What is the equation of the image?

Accepted Answer

y = -|x| - 2

Answer

y = |-x| - 2

Answer

y = |x - 2|

Answer

y = -|x| + 2

Question 14

The graph of y = 3x is reflected across the x-axis and shifted 7 units down. What is the equation of the image?

Accepted Answer

y = -3x - 7

Answer

y = -3x + 7

Answer

y = 3x - 7

Answer

y = -3-x - 7

Question 15

The blue curve is y = x^2 and the purple curve is its image under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = (1/4)x^2

Answer

y = 4x^2

Answer

y = (1/16)x^2

Answer

y = 16x^2

Question 16

The graph of y = x^2 is shifted 5 units left and 2 units up. What is the equation of the image?

Accepted Answer

y = (x + 5)^2 + 2

Answer

y = (x - 5)^2 + 2

Answer

y = (x + 5)^2 - 2

Answer

y = (x - 2)^2 - 5

Question 17

The graph of y = x is reflected across the x-axis and shifted 8 units up. What is the equation of the image?

Accepted Answer

y = -x + 8

Answer

y = x + 8

Answer

y = --x + 8

Question 18

The blue curve is y = x^3 and the purple curve is its image after a shift. What is the equation of the image?

Accepted Answer

y = (x - 3)^3 - 4

Answer

y = (x + 3)^3 - 4

Answer

y = (x - 3)^3 + 4

Answer

y = (x + 4)^3 + 3

Question 19

The graph of y = |x| is shifted 6 units right and 6 units down. What is the equation of the image?

Accepted Answer

y = |x - 6| - 6

Answer

y = |x + 6| - 6

Answer

y = |x - 6| + 6

Answer

y = |x + 6| + 6

Question 20

The graph of y = x is shifted 1 unit right and 7 units up. What is the equation of the image?

Accepted Answer

y = x - 1 + 7

Answer

y = x + 1 + 7

Answer

y = x - 1 - 7

Answer

y = x - 7 + 1

Question 21

An absolute value graph opens downward with its corner at (1, -5) and passes through (2, -8). What is its equation?

Accepted Answer

y = -3|x - 1| - 5

Answer

y = -3|x + 1| - 5

Answer

y = 3|x - 1| - 5

Answer

y = -|x - 1| - 5

Question 22

The graph of y = x is reflected across the x-axis and shifted 3 units up. What is the equation of the image?

Accepted Answer

y = -x + 3

Answer

y = x + 3

Answer

y = --x + 3

Question 23

The graph of y = |x| is reflected across the x-axis and shifted 3 units up. What is the equation of the image?

Accepted Answer

y = -|x| + 3

Answer

y = |-x| + 3

Answer

y = |x + 3|

Answer

y = -|x| - 3

Question 24

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = 2|x + 4| + 2

Answer

y = 2|x - 4| + 2

Answer

y = -2|x + 4| + 2

Answer

y = |x + 4| + 2

Question 25

The point (3, 9) on the graph of y = x^2 moves to (3, 27) under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = 3x^2

Answer

y = (1/3)x^2

Answer

y = 9x^2

Answer

y = (1/9)x^2

Question 26

The graph of y = x^3 is shifted 2 units left and 7 units up. What is the equation of the image?

Accepted Answer

y = (x + 2)^3 + 7

Answer

y = (x - 2)^3 + 7

Answer

y = (x + 2)^3 - 7

Answer

y = (x - 7)^3 - 2

Question 27

The blue curve is y = x^3 and the purple curve is its image under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = (1/2)x^3

Answer

y = 2x^3

Answer

y = (1/4)x^3

Answer

y = 4x^3

Question 28

The blue curve is y = x and the purple curve is its image after a shift. What is the equation of the image?

Accepted Answer

y = x - 4 - 6

Answer

y = x + 4 - 6

Answer

y = x - 4 + 6

Answer

y = x + 6 + 4

Question 29

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = -2|x - 5| - 1

Answer

y = -2|x + 5| - 1

Answer

y = 2|x - 5| - 1

Answer

y = -|x - 5| - 1

Question 30

The graph of y = |x| is reflected across the x-axis and shifted 4 units up. What is the equation of the image?

Accepted Answer

y = -|x| + 4

Answer

y = |-x| + 4

Answer

y = |x + 4|

Answer

y = -|x| - 4

Question 31

An absolute value graph opens downward with its corner at (-2, -1) and passes through (-1, -5). What is its equation?

Accepted Answer

y = -4|x + 2| - 1

Answer

y = -4|x - 2| - 1

Answer

y = 4|x + 2| - 1

Answer

y = -|x + 2| - 1

Question 32

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = -2|x + 2| - 1

Answer

y = -2|x - 2| - 1

Answer

y = 2|x + 2| - 1

Answer

y = -|x + 2| - 1

Question 33

The graph of y = x^3 is reflected across the y-axis and shifted 8 units up. What is the equation of the image?

Accepted Answer

y = (-x)^3 + 8

Answer

y = (-x)^3 - 8

Answer

y = (x + 8)^3

Answer

y = -(-x)^3 + 8

Question 34

The green curve is y = cbrt(x) and the purple curve is its image after a shift. What is the equation of the image?

Accepted Answer

y = cbrt(x - 6) - 1

Answer

y = cbrt(x + 6) - 1

Answer

y = cbrt(x - 6) + 1

Answer

y = cbrt(x + 1) + 6

Question 35

The graph of y = 3x is reflected across the x-axis and shifted 8 units up. What is the equation of the image?

Accepted Answer

y = -3x + 8

Answer

y = -3x - 8

Answer

y = 3x + 8

Answer

y = -3-x + 8

Question 36

The graph of y = x^3 is shifted 2 units left and 4 units down. What is the equation of the image?

Accepted Answer

y = (x + 2)^3 - 4

Answer

y = (x - 2)^3 - 4

Answer

y = (x + 2)^3 + 4

Answer

y = (x + 4)^3 - 2

Question 37

Use the graph of the absolute value function. What is its equation?

Accepted Answer

y = -4|x + 4| + 5

Answer

y = -4|x - 4| + 5

Answer

y = 4|x + 4| + 5

Answer

y = -|x + 4| + 5

Question 38

The point (4, 16) on the graph of y = x^2 moves to (4, 32) under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = 2x^2

Answer

y = (1/2)x^2

Answer

y = 4x^2

Answer

y = (1/4)x^2

Question 39

The graph of y = |x| is shifted 4 units right and 4 units down. What is the equation of the image?

Accepted Answer

y = |x - 4| - 4

Answer

y = |x + 4| - 4

Answer

y = |x - 4| + 4

Answer

y = |x + 4| + 4

Question 40

The point (4, 16) on the graph of y = x^2 moves to (4, 8) under a single vertical stretch or compression. What is the equation of the image?

Accepted Answer

y = (1/2)x^2

Answer

y = 2x^2

Answer

y = (1/4)x^2

Answer

y = 4x^2

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Writing a Transformed Function

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Writing a Transformed Function

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