Question 1

Which of the following describes a relation that is also a function?

Accepted Answer

Each element in the domain is paired with exactly one element in the range.

Answer

One element in the domain is paired with multiple elements in the range.

Answer

Elements in the range are not paired with any element in the domain.

Answer

Each element in the range is paired with exactly one element in the domain.

Question 2

Which of the following graphs represents a function?

Accepted Answer

A graph where any vertical line intersects it at most once.

Answer

A graph where any vertical line intersects it exactly twice.

Answer

A graph where any horizontal line intersects it multiple times.

Answer

A graph where every point is connected by a vertical line.

Question 3

Which of the following sets of ordered pairs represents a relation that is not a function?

Accepted Answer

{(1, 2), (1, 3), (2, 4)}

Answer

{(1, 2), (2, 3), (3, 4)}

Answer

{(0, 1), (1, 2), (2, 3)}

Answer

{(2, 3), (3, 4), (4, 5)}

Question 4

For the functions f(x) = 2x and g(x) = x + 3, what is (f / g)(x)?

Accepted Answer

2x / (x + 3)

Answer

2 / (x + 3)

Answer

2x / 3

Answer

2x + 3

Question 5

Given the functions

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

2x^2 + 1

Answer

x^2 + 2x + 3

Answer

2x^2 + 3

Answer

2x^2 - 1

Question 6

What is the value of the function

f(x) = 2x + 3

when

g(x) = x^2 - 1

?

Accepted Answer

undefined

Answer

0

Answer

5

Answer

2

Question 7

If

f(x) = 2x + 3

, for which value of

g(x) = x^2 - 1

is

(f \circ g)(x)

undefined?

Accepted Answer

-2

Answer

-4

Answer

2

Answer

0

Question 8

If

f(x) = 2x + 3

, what is the simplified form of

g(x) = x^2 - 1

?

Accepted Answer

x + 1

Answer

\frac{1}{x(x - 1)}

Answer

x^2 - 1

Answer

x - 1

Question 9

If

f(x) = 2x + 3

, for which value of

g(x) = x^2 - 1

is

(f \circ g)(x)

undefined?

Accepted Answer

3

Answer

1

Answer

2

Answer

-3

Question 10

What is the value of f(g(x)) if f(x) = 2x + 3 and g(x) = x - 1?

Accepted Answer

2(x - 1) + 3

Answer

2(x + 1) + 3

Answer

2(x - 3) + 1

Answer

x + 2

Question 11

Which of the following is a function?

Accepted Answer

A relation where each input has exactly one output

Answer

A relation with no inputs or outputs

Answer

A relation where inputs can have multiple outputs

Answer

A relation where each output is related to multiple inputs

Question 12

If

f(x) = 2x + 3

, what is

g(x) = x^2 - 1

?

Accepted Answer

11

Answer

7

Answer

12

Answer

8

Question 13

Which of the following sets of ordered pairs represents a function?

Accepted Answer

{(1, 2), (2, 3), (3, 4)}

Answer

{(2, 2), (3, 3), (2, 4)}

Answer

{(1, 2), (1, 3), (2, 4)}

Answer

{(1, 2), (2, 3), (3, 3), (2, 5)}

Question 14

If

f(x) = 2x + 3

, what is the value of

g(x) = x^2 - 1

?

Accepted Answer

2.5

Answer

1.5

Answer

3.5

Answer

2

Question 15

Which of the following represents a one-to-one function?

Accepted Answer

Each input has one unique output, and each output is paired with only one input.

Answer

Each input has multiple outputs.

Answer

Each output can be paired with multiple inputs.

Answer

Both inputs and outputs can have multiple pairings.

Question 16

Which of the following is a characteristic of a function?

Accepted Answer

Each input is mapped to exactly one output.

Answer

Each output can be mapped to multiple inputs.

Answer

Each output must be a positive number.

Answer

Each input can be mapped to multiple outputs.

Question 17

Which of the following relations is not a function?

Accepted Answer

A relation where one input is mapped to multiple outputs.

Answer

A relation where inputs are mapped to outputs in a one-to-one manner.

Answer

A relation where each input is mapped to one unique output.

Answer

A relation where each output is mapped to one input.

Question 18

Which of the following defines a relation that is not a function?

Accepted Answer

A set of ordered pairs where some inputs map to multiple outputs.

Answer

A set of ordered pairs where each input maps to exactly one output.

Answer

A set of ordered pairs where each output maps to exactly one input.

Answer

A set of ordered pairs where no input is repeated.

Question 19

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

f(g(x)) = (x - 3)^2

Answer

g(f(x)) = x^2 - 9

Answer

f(g(x)) = x^2 - 3

Answer

g(f(x)) = x^2 - 3

Question 20

Which of the following statements is true for the relation defined by the set of ordered pairs

f(x) = 2x + 3

?

Accepted Answer

It is a function because each input has exactly one output

Answer

It is not a function because there are repeating inputs

Answer

It is not a function because there are repeating outputs

Answer

It is a function because each output has exactly one input

Question 21

Given the function

f(x) = 2x + 3

, what is

g(x) = x^2 - 1

?

Accepted Answer

11

Answer

13

Answer

8

Answer

10

Question 22

Which of the following sets of ordered pairs represents a function?

Accepted Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Question 23

Which of the following statements is true about the vertical line test?

Accepted Answer

A graph represents a function if and only if no vertical line intersects the graph at more than one point

Answer

A graph represents a function if any vertical line intersects the graph at most three points

Answer

A graph represents a function if a vertical line intersects the graph at least once

Answer

A graph represents a function if any vertical line intersects the graph at exactly two points

Question 24

For the function

f(x) = 2x + 3

, what is

g(x) = x^2 - 1

?

Accepted Answer

11

Answer

5

Answer

7

Answer

9

Question 25

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

11

Answer

10

Answer

4

Answer

9

Question 26

Given

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

5

Answer

-2

Answer

3

Answer

7

Question 27

Given the functions

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

6

Answer

12

Answer

8

Answer

10

Question 28

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

4

Answer

2

Answer

10

Answer

6

Question 29

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

-4

Answer

2

Answer

-6

Answer

0

Question 30

Given the functions

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

7

Answer

4

Answer

6

Answer

5

Question 31

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

63

Answer

21

Answer

36

Answer

27

Question 32

Given the functions

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

-2

Answer

0

Answer

5

Answer

1

Question 33

If

f(x) = 2x + 3

and

g(x) = x^2 - 1

, what is

(f \circ g)(x)

?

Accepted Answer

2

Answer

8

Answer

6

Answer

0

Question 34

For the rational function

f(x) = 2x + 3

, what is/are the vertical asymptote(s)?

Accepted Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Question 35

What is the horizontal asymptote of the rational function

f(x) = 2x + 3

?

Accepted Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Question 36

For the rational function

f(x) = 2x + 3

, what are the x-intercepts?

Accepted Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Answer

\{ (1,2), (2,3), (3,4), (4,5) \}

Question 37

What is the reason that the rational function

f(x) = 2x + 3

cannot be solved for

g(x) = x^2 - 1

?

Accepted Answer

It leads to division by zero

Answer

It has no real solutions

Answer

It produces an undefined equation

Answer

It results in complex numbers

Question 38

In the rational function

f(x) = 2x + 3

, what values of

g(x) = x^2 - 1

make the function undefined?

Accepted Answer

x = 2 and x = -2

Answer

x = 1 and x = -1

Answer

x = 0

Answer

x = 4 and x = -4

Question 39

Why can't the rational function

f(x) = 2x + 3

be undefined for any real number

g(x) = x^2 - 1

?

Accepted Answer

The denominator is never zero

Answer

The function can become imaginary

Answer

The numerator cancels with the denominator

Answer

The numerator is always positive

Question 40

For the rational function

f(x) = 2x + 3

, why is the function undefined at

g(x) = x^2 - 1

?

Accepted Answer

The denominator equals zero

Answer

The function becomes imaginary

Answer

The numerator equals zero

Answer

The numerator and denominator cancel out

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