Free Printable AP Transformations

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AP Transformations

Total questions: 18

Worksheet time: 13mins

Name

Class

Date

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

Translation left 2 units

Translation right 2 units

Vertical translation up by 2 units.

Reflection across the x-axis.

How did the equation shift from the parent function? y = f(x - 4)

Shift right by 4

Shift left by 4

Horizontal Stretch by 4

Vertical Stretch by 4

Shift down by 4

Describe the transformation of y = (x - 4)²

Shift UP

Shift DOWN

Shift LEFT

Shift RIGHT

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

f(-2x - 4)

f(-1/2x) - 4

-f(2x) - 4

-f(1/2x) - 4

Which of the following is the correct equation for the given graph?

f(x) = (x - 2)² - 1

f(x) = (x + 2)² - 1

f(x) = -(x + 2)² - 1

f(x) = -(x - 2)² - 1

Which of the following is the correct equation for the given graph?

f(x) = -(x + 2)² - 4

f(x) = -(x - 2)² - 4

f(x) = -3(x - 2)² - 4

f(x) = -3(x + 2)² - 4

What type of function is shown?

cube root

square root

logarithm

exponential

What is the equation of the graph below?

f(x ) = I x + 4 I + 2

f(x ) = -I x - 4 I + 2

f(x ) = I x - 4 I + 2

f(x ) = -I x + 4 I + 2

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

y = -|x + 2| - 7

y = |x - 2| - 7

y = -|x - 2| - 7

y = -|x - 2| + 7

10.

What transformations has the function undergone?

reflect over y, vertical compress by 2, right 5, up 1

reflect over x, horizontal compression by 2, left 5, up 1

reflect over x, vertical stretch by 2, right 5, up 1

reflect over y, horizontal stretch by -2, right 5, up 1

11.

Which of the following transformation has NOT been applied to the function

$f\left(x\right)=\left|-3x\right|-1$

Y axis reflection

Down 1

Right 3

Horizontal compression by 1/3

12.

Which function is described by the graph shown?

(assume no stretches or compressions)

$y=\frac{1}{x+3}-1$

$y=\frac{1}{x-3}-1$

$y=-\frac{1}{x+3}-1$

$y=-\frac{1}{x-3}-1$

13.

𝑓(𝑥) = 𝑥² + 3𝑥 − 5

𝑔(𝑥) = −𝑓(4𝑥) , find 𝑔(𝑥).

g(x) = -16x² - 12x + 5

g(x) = -4x² - 12x + 5

g(x) = -4x² - 3x + 5

g(x) = -4x³ - 12x² + 20x

14.

𝑓(𝑥) = 2𝑥² + 4𝑥 − 3

𝑔(𝑥) = 3𝑓(𝑥) − 5 , find 𝑔(𝑥)

g(x) = 6x² + 12x - 14

g(x) = 18x² + 12x - 8

g(x) = 6x² + 12x - 8

g(x) = 5x² + 9x - 14

15.

D: (-20, 8]

R: [-2, 16]

D: (-5, 2]

R: [-2, 16]

D: (-5, 2]

R: [-10, 8]

D: (-20, 8]

R: [-10, 8]

16.

D: [-2, 5]

R: (-13, -3)

D: [-2, 5]

R: (-3, -13)

D: [-18, 45]