Free Printable Functions and Transformations Review

1.

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

a)

y = -|x + 2| - 7

b)

y = |x - 2| - 7

c)

y = -|x - 2| - 7

d)

y = -|x - 2| + 7

2.

Describe the transformation that is applied to the parent function.
f(x) = IxI -5

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

3.

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

4.

Choose the correct translated function.

a)

f(x)= |x|+2

b)

f(x)= |x|-2

c)

f(x)= -|x|

d)

f(x)= -|x|+2

5.

Choose the graph that matched the equation.
y = |x - 1|

a)

b)

c)

d)

6.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

7.

What is the range of this function?

a)

[-4,∞)

b)

[0, ∞)

c)

(-∞, 4]

d)

(0,∞)

8.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

9.

a)

y = −√(x) − 3

b)

y = −√(x − 3)

c)

y = √(x) − 3

d)

y = √(x − 3)

10.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

Pickle

11.

Find the domain and range of:
$f(x)=\log_2(x)$

a)

Domain: $\left(-\infty,\infty\right)$
Range: $\left(0,\infty\right)$

b)

Domain: $null$
Range: $\left(-\infty,\infty\right)$

c)

Domain: $\left(0,\infty\right)$
Range: undefined

d)

Domain: $null$
Range: $\left(-\infty,0\right)$

12.

Describe range of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

13.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

14.

What is the asymptote for the logarithmic function

$f\left(x\right)=\log\left(x-2\right)$

a)

x = 2

b)

x = -2

c)

y = 2

d)

y = -2

15.

This graph is _______________.

a)

increasing

b)

decreasing

16.

Asymptote?

a)

y = 2

b)

y = -2

c)

x = 2

d)

y = 0

17.

Domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

(-∞, 0)

d)

[0, ∞)

18.

Range?

a)

(-8, ∞)

b)

[-8, ∞)

c)

(-∞, ∞)

d)

(∞, -8)

19.

Positive?

a)

(-2, ∞)

b)

(-∞, -2)

c)

(-∞, ∞)

d)

N/A

20.

Negative?

a)

(-2, ∞)

b)

(-∞, -2)

c)

(-∞, ∞)

d)

N/A

21.

Exponential Growth or Decay?

a)

Exponential Growth

b)

Exponential Decay

c)

Both Growth & Decay

d)

Cannot be Determined

22.

y-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(1.2, 0)

d)

(0, 1.2)

23.

x-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(1.2, 0)

d)

(0, 1.2)

24.

Asymptote?

a)

y = 4

b)

y = 0

c)

x = 4

d)

y = 5

25.

Range?

a)

(-∞, 2)

b)

(-∞, 2]

c)

(2, ∞)

d)

(2, -∞)

26.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

27.

Compared to the graph of $y=\log_2x$ , the asymptote of $y=\log_2x+1$ will translate...

a)

right one to x = 1

b)

left one to x = -1

c)

no observable translation, and will remain x = 0

28.

Which function matches the graph?

a)

A

f(x) = ∛(x + 3) + 2

b)

B

f(x) = − ∛(x - 3) + 2

c)

C

f(x) = ∛(x - 3) + 2

d)

D

f(x) = ∛(x - 2) + 3

29.

Which function matches the graph?

a)

A

f(x) = − ∛(x + 3) − 1

b)

B

f(x) = − ∛(x - 3) − 1

c)

C

f(x) = ∛(x + 3) − 1

d)

D

f(x) = ∛(x - 1) + 3

30.

Describe the transformation.

a)

Down 1

b)

Reflect over y-axis

c)

Up 1

d)

Reflect over x-axis

31.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

e)

linear

32.

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

a)

Vertical stretch by a factor of 2

b)

Vertical compression by a factor of 1/2

c)

Vertical translation up by 2 units.

d)

Horizontal compression by a factor of 1/2

33.

Determine the Domain

a)

x > 5

b)

x > -5

c)

All Reals

d)

x > 1

34.

Determine the Range of the function

a)

All Reals

b)

y > 2

c)

x > 3

d)

y < 2

35.

Which function is graphed? You can click on the image to see an enlarged view.

a)

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

b)

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

c)

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

d)

f(x) = -2|x - 4|

36.

Which function is graphed? You can click on the image to see an enlarged view.

a)

f(x) = -2|x - 3| + 5

b)

f(x) = -|x + 5| - 3

c)

f(x) = -2|x + 3| + 5

d)

f(x) = -2|x + 5| - 3

37.

Identify the Transformations.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

38.

What transformations has the function undergone?

a)

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

b)

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

c)

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

d)

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

39.

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

40.

What is the equation of the graph?

a)

$y=\sqrt{x+3}$

b)

$y=-\sqrt{x+3}$

c)

$y=-\sqrt{x}+3$

d)

$y=\sqrt{x}+3$

41.

a)

$y=-\sqrt{x+1}$

b)

$y=\sqrt{x+1}$

c)

$y=-\sqrt{x}-1$

d)

$y=\sqrt{x}+1$

42.

Match the correct equation with the given graph.

a)

$y=\sqrt{x}+2$

b)

$y=\sqrt{x}-2$

c)

$y=\sqrt{x+2}$

d)

$y=\sqrt{x-2}$

43.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

44.

Write the equation of the function f(x)=3logx+4 after the following transformations:

Vertical stretch by a factor of 2, translate 5 units to the right.

a)

g(x)=5log(x+5)+4

b)

g(x)=5log(x-5)+4

c)

g(x)=6log(x-1)

d)

g(x)=6log(x-5)+4

Functions and Transformations Review

Total questions: 44

Worksheet time: 1hrs 25mins

Similar Resources on Wayground