Functions: A Comprehensive Guide for 8th Grade Math Students

Question 1

To determine the rate of change of a linear function, what should you calculate?

Accepted Answer

The slope of the graph

Answer

The difference between the y-intercepts

Answer

The average of the x- and y-values

Answer

The ratio of the y-values to the x-values

Question 2

Find the inverse function of f(x) = 2x + 3.

Accepted Answer

f^-1(x) = (x-3)/2

Answer

f^-1(x) = 3x + 2

Answer

f^-1(x) = -2x - 3

Answer

f^-1(x) = 2x - 3

Question 3

Which equation represents a quadratic function?

Accepted Answer

y = x^2 - 5x + 6

Answer

y = 3x + 2

Answer

y = e^x

Answer

y = log(x)

Question 4

Which of the following is an example of an exponential function?

Accepted Answer

y = 5^x

Answer

y = 2x + 3

Answer

y = x^3 - 2x + 1

Answer

y = 1/x

Question 5

What is the equation of the exponential function with a base of 3 and a y-intercept of 2?

Accepted Answer

y = 3^x + 2

Answer

y = 2^x + 3

Answer

y = x^3 + 2

Answer

y = 3x + 2

Question 6

Which of the following is not a characteristic of linear functions?

Accepted Answer

Can have a maximum or minimum point

Answer

Constant rate of change

Answer

Graph is a straight line

Answer

Output is always proportional to the input

Question 7

What is the inverse of the function y = 2x + 1?

Accepted Answer

y = (x - 1)/2

Answer

y = 2x - 1

Answer

y = 1/2x + 1

Answer

y = -2x + 1

Question 8

What is the average rate of change of the function y = x^3 on the interval [1, 3]?

Accepted Answer

9

Answer

1

Answer

3

Answer

27

Question 9

What is the slope of the line with the equation y = 2x + 1?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 10

Which of the following functions is concave up?

Accepted Answer

y = x^2

Answer

y = -x^2

Answer

y = 3^-x

Answer

y = sin(x)

Question 11

What is the domain of the function f(x) = sqrt(x)?

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 12

Which of the following functions is an odd function?

Accepted Answer

y = sin(x)

Answer

y = x^2

Answer

y = 2x + 1

Answer

y = 3^-x

Question 13

What is the domain of the function f(x) = x + 5?

Accepted Answer

All real numbers

Answer

All integers

Answer

All positive numbers

Answer

All negative numbers

Question 14

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

An ellipse

Question 15

What is the y-intercept of the line with the equation y = 2x + 3?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 16

Which of the following is an example of an exponential function?

Accepted Answer

f(x) = 2^x

Answer

f(x) = x^2

Answer

f(x) = sin(x)

Answer

f(x) = cos(x)

Question 17

Which of the following is a real-world example of a quadratic function?

Accepted Answer

The trajectory of a thrown ball

Answer

The growth of a population

Answer

The temperature of a cup of coffee as it cools

Answer

The distance traveled by a car

Question 18

A function is a relation where:

Accepted Answer

Each input corresponds to exactly one output.

Answer

Multiple inputs can map to the same output.

Answer

The input and output are always equal.

Answer

The relation is represented by a graph.

Question 19

A bacterial culture starts with 1,000 bacteria and doubles every hour. Write an exponential function to model this growth. Use the function to predict the population after 5 and 10 hours.

Accepted Answer

f(x) = 1000 * 2^x

Answer

f(x) = 1000 + 2x

Answer

f(x) = 1000 * (1/2)^x

Answer

f(x) = 1000 * x^2

Question 20

Which of the following is a linear function?

Accepted Answer

y = 5x - 3

Answer

y = 2x^2 + 1

Answer

y = x^3 + 2x

Answer

y = cos(x)

Question 21

Find the slope of the line passing through the points (2, 5) and (4, 9).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 22

What type of graph represents a quadratic function?

Accepted Answer

Parabola

Answer

Straight line

Answer

Circle

Answer

Ellipse

Question 23

Find the vertex of the parabola y = x^2 - 4x + 3.

Accepted Answer

(2, -1)

Answer

(1, -2)

Answer

(3, 0)

Answer

(4, 1)

Question 24

Which of the following is an exponential function?

Accepted Answer

y = 3^x

Answer

y = 2x + 1

Answer

y = x^2 - 2

Answer

y = sin(x)

Question 25

Find the inverse of the function f(x) = 2x + 3.

Accepted Answer

f^(-1)(x) = (x - 3)/2

Answer

f^(-1)(x) = 3 - 2x

Answer

f^(-1)(x) = 2x - 3

Answer

f^(-1)(x) = 1/(2x + 3)

Question 26

Write the equation of the line with a slope of -2 and a y-intercept of 3.

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -3x + 2

Answer

y = 3x + 2

Question 27

Determine the domain of the exponential function y = 2^x.

Accepted Answer

All real numbers

Answer

Only positive numbers

Answer

Only non-zero numbers

Answer

Only integers

Question 28

Find the inverse of the function f(x) = 3x + 5.

Accepted Answer

f^-1(x) = (x - 5)/3

Answer

f^-1(x) = (x + 5)/3

Answer

f^-1(x) = 3x - 5

Answer

f^-1(x) = 5x + 3

Question 29

Which statement is NOT a true property of a function?

Accepted Answer

The graph of a function can take any shape.

Answer

Each input value corresponds to exactly one output value.

Answer

The relationship between the input and output is constant.

Answer

The output value can be any real number.

Question 30

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

An exponential curve

Question 31

What is the slope-intercept form of the equation of a linear function?

Accepted Answer

y = mx + b

Answer

y = ax^2 + bx + c

Answer

y = e^x

Answer

y = log(x)

Question 32

What is the domain of the exponential function f(x) = 2^x?

Accepted Answer

All real numbers

Answer

Positive real numbers

Answer

Negative real numbers

Answer

Real numbers greater than 1

Question 33

Which function is a one-to-one function?

Accepted Answer

f(x) = e^x

Answer

f(x) = x^2

Answer

f(x) = |x|

Answer

f(x) = sin(x)

Question 34

Find the range of the function f(x) = -|x|.

Accepted Answer

{y | y ≤ 0}

Answer

{y | y ≥ 0}

Answer

{y | y ≠ 0}

Answer

{y | y = 0}

Question 35

Provide an example of a linear function.

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2x + 1

Answer

y = e^x

Answer

y = sin(x)

Question 36

Describe the graph of a quadratic function.

Accepted Answer

It possesses all of the above characteristics.

Answer

It takes the shape of a parabola.

Answer

It exhibits a maximum or minimum point.

Answer

It opens either upward or downward.

Question 37

What is the domain of the exponential function y = 2^x?

Accepted Answer

All real numbers

Answer

Positive real numbers only

Answer

Negative real numbers only

Answer

Integers only

Question 38

Express the equation y = log2(x) in an equivalent form.

Accepted Answer

x = 2^y

Answer

y = 2x

Answer

x = log(2y)

Answer

y = log(2x)

Question 39

Find the range of the function y = |x|.

Accepted Answer

Zero and positive real numbers only

Answer

All real numbers

Answer

Positive real numbers only

Answer

Negative real numbers only

Question 40

Determine the inverse of the function: y = 2x - 3

Accepted Answer

y = (x + 3)/2

Answer

y = 2x + 3

Answer

y = 3 - 2x

Answer

None of these

Question 41

Find the slope of the line represented by the equation: y = 2x + 3?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 42

What is the domain of the exponential function: f(x) = 2^x?

Accepted Answer

All real numbers

Answer

All positive numbers

Answer

All negative numbers

Answer

Only integers

Question 43

Which of the following functions is increasing?

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = -x^2

Answer

y = 1/x

Question 44

Find the inverse of the function: f(x) = 3x - 5?

Accepted Answer

f^-1(x) = (x + 5)/3

Answer

f^-1(x) = 3x + 5

Answer

f^-1(x) = 1/3x + 5

Answer

f^-1(x) cannot be determined

Question 45

Which of the following is a composite function?

Accepted Answer

f(x) = g(h(x))

Answer

f(x) = x^2

Answer

f(x) = sin(x)

Answer

f(x) = x + 2

Question 46

Find the slope of the line given by the equation y = 2x + 3.

Accepted Answer

2

Answer

3

Answer

-3

Answer

-2

Question 47

Identify the quadratic function among the following options:

Accepted Answer

y = x^2

Answer

y = 2x + 1

Answer

y = e^x

Answer

y = sin(x)

Question 48

Determine the vertex of the parabola represented by the equation y = (x - 2)^2 + 1.

Accepted Answer

(2, 1)

Answer

(-2, 1)

Answer

(2, -1)

Answer

(1, 2)

Question 49

Which characteristic describes exponential functions?

Accepted Answer

They increase rapidly as x increases

Answer

They are linear functions

Answer

They decrease rapidly as x increases

Question 50

Identify the domain of the function f(x) = sqrt(x):

Accepted Answer

x ≥ 0

Answer

x < 0

Answer

All real numbers

Answer

x > 0

Question 51

Which definition describes a function?

Accepted Answer

A relation where each input corresponds to exactly one output

Answer

A set of ordered pairs

Answer

A relation where each output corresponds to exactly one input

Question 52

Find the inverse of the function f(x) = 2x + 1:

Accepted Answer

f^-1(x) = (x - 1)/2

Answer

f^-1(x) does not exist

Answer

f^-1(x) = x^2 - 1

Answer

f^-1(x) = 1/2x

Question 53

Determine the range of the function f(x) = |x|:

Accepted Answer

y ≥ 0

Answer

y < 0

Answer

y > 0

Answer

All real numbers

Question 54

Which of the following is the graph of a linear function?

Accepted Answer

A straight line that continues indefinitely in both directions.

Answer

A parabola that opens either upward or downward.

Answer

A circle that forms a closed loop.

Question 55

Which of the following represents the equation of a line with a slope of -2 and a y-intercept of 1?

Accepted Answer

y = -2x + 1

Answer

y = x + 1

Answer

y = -x + 1

Answer

y = 2x - 1

Question 56

Which of the following is a quadratic function?

Accepted Answer

f(x) = x² + 2x - 1

Answer

f(x) = 1/x

Answer

f(x) = eˣ

Answer

f(x) = √x

Question 57

Which of the following is an exponential function?

Accepted Answer

f(x) = 2ˣ

Answer

f(x) = log(x)

Answer

f(x) = sin(x)

Answer

f(x) = x³

Question 58

Determine the domain of the exponential function f(x) = e^(-x).

Accepted Answer

All real numbers

Answer

x > 0

Answer

x ≥ 0

Answer

x < 0

Question 59

Which of the following represents the graph of the function f(x) = |x|?

Accepted Answer

A V-shaped graph with a sharp point at the origin and two straight line segments extending in opposite directions.

Answer

A sinusoidal graph that oscillates above and below a central axis.

Answer

A parabolic graph that opens upward.

Answer

A linear graph that forms a straight line.

Question 60

What is the domain of the function f(x) = 2x - 5?

Accepted Answer

All real numbers

Answer

Only rational numbers

Answer

Only positive integers

Answer

Only negative integers

Question 61

Which of the following is the graph of a quadratic function?

Accepted Answer

A parabola

Answer

An ellipse

Answer

A straight line

Answer

A circle

Question 62

What is the slope of the line represented by the equation y = -3x + 2?

Accepted Answer

-3

Answer

-2

Answer

3

Answer

2

Question 63

Which of the following is the y-intercept of the function f(x) = 3x + 1?

Accepted Answer

1

Answer

3

Answer

-1

Answer

0

Question 64

What is the vertex of the parabola represented by the equation y = (x - 2)^2 + 1?

Accepted Answer

(2, 1)

Answer

(-2, 1)

Answer

(0, 0)

Answer

(1, 2)