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Free Practice Quiz Question List

01 Functions and Their Graphs Online Quiz Questions

Use this free practice quiz with 20 questions to review 01 Functions and Their Graphs, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose all
1 point

Select all statements that correctly characterize a function of xx.

  1. A

    Each allowed input is paired with exactly one output.

  2. B

    Different inputs must always produce different outputs.

  3. C

    Every vertical line intersects the graph at most once.

  4. D

    Every horizontal line intersects the graph at most once.

02
True or false
1 point

True or false: In the composition (f∘g)(x)=f(g(x))(f\circ g)(x)=f(g(x)), the function ff is applied before the function gg.

  1. A

    True

  2. B

    False

03
Written response
1 point

Given f(x)=3x−7f(x)=3x-7, what is f(5)f(5)?

04
Fill in the blank
1 point

Complete the statement: For h(x)=1x+2h(x)=\frac{1}{x+2}, the value x=x= must be excluded from the domain.

05
Choose one
1 point

If f(x)=2x+3f(x)=2x+3, which equation gives f−1(x)f^{-1}(x)?

  1. A

    f−1(x)=2x−3f^{-1}(x)=2x-3

  2. B

    f−1(x)=x+32f^{-1}(x)=\frac{x+3}{2}

  3. C

    f−1(x)=x−32f^{-1}(x)=\frac{x-3}{2}

  4. D

    f−1(x)=2x−3f^{-1}(x)=\frac{2}{x-3}

06
Choose all
1 point

Let ff be a parent function and define g(x)=−12f(x+3)−2g(x)=-\frac{1}{2}f(x+3)-2. Select all transformations used to obtain the graph of gg from the graph of ff.

  1. A

    Shift left 3 units.

  2. B

    Reflect across the xx-axis.

  3. C

    Compress vertically by a factor of 12\frac{1}{2}.

  4. D

    Shift downward 2 units.

  5. E

    Shift right 3 units.

  6. F

    Stretch vertically by a factor of 2.

07
True or false
1 point

True or false: The function f(x)=x2f(x)=x^2 is one-to-one on the real numbers.

  1. A

    True

  2. B

    False

08
Written response
1 point

What is the x-coordinate of the vertex of g(x)=−2(x−5)2+1g(x)=-2(x-5)^2+1?

09
Open ended
1 point

Let f(x)=xf(x)=\sqrt{x} and g(x)=x−3g(x)=x-3. Find (f∘g)(x)(f\circ g)(x) and state its domain. Explain why that domain is required.

10
Choose one
1 point

What is the y-intercept of f(x)=x2−6x+5f(x)=x^2-6x+5?

  1. A

    (5,0)(5,0)

  2. B

    (0,5)(0,5)

  3. C

    (−1,0)(-1,0)

  4. D

    (0,−5)(0,-5)

11
Fill in the blank
1 point

Complete the statement: The domain of f−1f^{-1} is the of ff.

12
Choose one
1 point

Which graphical test determines whether a function is one-to-one?

  1. A

    The vertical line test

  2. B

    The slope test

  3. C

    The horizontal line test

  4. D

    The endpoint test

13
True or false
1 point

True or false: If every vertical line intersects a graph at most once, then the graph represents a function of xx.

  1. A

    True

  2. B

    False

14
Choose one
1 point

If f(x)=x2−4x+1f(x)=x^2-4x+1, what is f(3)f(3)?

  1. A

    −4-4

  2. B

    22

  3. C

    −2-2

  4. D

    1414

15
Written response
1 point

Let f(x)=2x+1f(x)=2x+1 and g(x)=x2g(x)=x^2. Enter the value of (f∘g)(3)(f\circ g)(3).

16
Choose one
1 point

Relative to the graph of y=f(x)y=f(x), what transformation produces g(x)=f(x−3)g(x)=f(x-3)?

  1. A

    Three units left

  2. B

    Three units right

  3. C

    Three units up

  4. D

    Three units down

17
Written response
1 point

For f(x)=3x−5f(x)=3x-5, enter the value of f−1(4)f^{-1}(4).

18
Choose one
1 point

How is the graph of f−1f^{-1} related to the graph of ff?

  1. A

    Reflect the graph across y=xy=x

  2. B

    Reflect the graph across the xx-axis

  3. C

    Shift the graph one unit upward

  4. D

    Rotate the graph 90∘90^\circ about the origin

19
Choose one
1 point

What is the maximum value of g(x)=−2(x−1)2+4g(x)=-2(x-1)^2+4?

  1. A

    44

  2. B

    22

  3. C

    −2-2

  4. D

    11

20
Choose one
1 point

What is the real-valued domain of h(x)=log⁡(x−1)+5−xh(x)=\log(x-1)+\sqrt{5-x}?

  1. A

    [1,5]

  2. B

    (1,5]

  3. C

    (-\infty,1)\cup[5,\infty)

  4. D

    (1,\infty)