Functions: Interactive Learning Quizzes for 7th Grade Math

Question 1

In the real world, what practical situation can be modeled using a quadratic function?

Accepted Answer

The path of a thrown ball

Answer

The area of a circle

Answer

The future value of an investment

Answer

The volume of a cone

Question 2

What happens to the graph of a function when it is translated vertically?

Accepted Answer

It shifts up or down.

Answer

It becomes narrower or wider.

Answer

It flips over the x or y-axis.

Answer

It moves left or right.

Question 3

Which type of symmetry is NOT a property of functions?

Accepted Answer

Asymmetric

Answer

Even

Answer

Odd

Answer

Periodic

Question 4

Which of the following is NOT a practical application of functions in the real world?

Accepted Answer

Solving crossword puzzles

Answer

Predicting population growth

Answer

Calculating distance traveled

Answer

Determining the rate of chemical reactions

Question 5

Which of the following is not a type of function?

Accepted Answer

Circle

Answer

Linear function

Answer

Quadratic function

Answer

Exponential function

Question 6

Identify the function that is a quadratic function.

Accepted Answer

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

Answer

f(x) = e^(2x)

Answer

f(x) = sqrt(x)

Answer

f(x) = |x - 1|

Question 7

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

Accepted Answer

f(x) = 3^x

Answer

f(x) = x^3

Answer

f(x) = sin(x)

Answer

f(x) = sqrt(x)

Question 8

Identify the range of the function g(x) = |x + 1|.

Accepted Answer

Only non-negative real numbers

Answer

All real numbers

Answer

Only positive real numbers

Answer

Only negative real numbers

Question 9

Which of the following equations represents a linear function in slope-intercept form?

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = e^x

Answer

y = |x|

Question 10

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

Accepted Answer

-3

Answer

1

Answer

2

Answer

-2

Question 11

Which of the following functions best models the decay of a radioactive substance over time?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Constant

Question 12

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 13

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

Accepted Answer

-2

Answer

2

Answer

3

Answer

-3

Question 14

Which of the following functions is an exponential function?

Accepted Answer

f(x) = 2^x

Answer

f(x) = x^2

Answer

f(x) = x + 1

Answer

f(x) = sin(x)

Question 15

Which of the following transformations will shift the graph of the function f(x) = x^2 to the left by 2 units?

Accepted Answer

f(x - 2)

Answer

f(x + 2)

Answer

f(2x)

Answer

f(x/2)

Question 16

The slope of a linear function describes:

Accepted Answer

The change in the y-value for every unit change in the x-value

Answer

The y-intercept of the function

Answer

The maximum value of the function

Answer

The domain of the function

Question 17

Which equation represents an exponential function?

Accepted Answer

y = 2^(3x)

Answer

y = 2x + 1

Answer

y = x^2 - 3

Answer

y = 1/x

Question 18

The graph of a function forms a parabola. What type of function is it?

Accepted Answer

Quadratic

Answer

Linear

Answer

Exponential

Answer

Piecewise

Question 19

The function f(x) = |x| is an example of a(n) function:

Accepted Answer

Absolute value function

Answer

Quadratic function

Answer

Exponential function

Answer

Step function

Question 20

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

Accepted Answer

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

Answer

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

Answer

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

Answer

f^(-1)(x) does not exist

Question 21

Which of the following functions is a one-to-one function?

Accepted Answer

f(x) = 2x + 1

Answer

f(x) = x^2

Answer

f(x) = |x|

Answer

f(x) = sin(x)

Question 22

Which of the following equations represents a linear function? A linear function has a constant rate of change.

Accepted Answer

y = 2x + 5

Answer

y = x^2 + 3

Answer

y = 3x^3 - 2x

Answer

y = 1/(x-1)

Question 23

What is the slope of the line with the equation y = -2x + 3? The slope tells you how steep a line is.

Accepted Answer

-2

Answer

3

Answer

1/2

Answer

-1/2

Question 24

Which of the following functions is an exponential function? An exponential function has a constant percent rate of change.

Accepted Answer

y = 2^x

Answer

y = x^2 + 1

Answer

y = 3x - 5

Answer

y = 1/(x+1)

Question 25

Which of the following is a vertical asymptote of the function f(x) = 1/(x-3)? A vertical asymptote is a vertical line that the graph of a function approaches but never touches.

Accepted Answer

x = 3

Answer

x = 0

Answer

y = 3

Answer

y = 0

Question 26

Which of the following is a composite function? A composite function is a function that is made up of two or more simpler functions.

Accepted Answer

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

Answer

f(x) = x^2

Answer

f(x) = 2x + 3

Answer

f(x) = sin(x)

Question 27

Which transformation shifts the graph of f(x) = 2x + 1 up by 3 units and to the right by 2 units?

Accepted Answer

f(x + 2) + 3

Answer

f(x - 2) + 3

Answer

f(x + 3) + 2

Question 28

How do the slope and y-intercept of a linear function affect its graph and real-life uses?

Accepted Answer

The slope determines the graph's slant, and the y-intercept sets its starting point.

Answer

Only the y-intercept determines the graph's starting point.

Answer

Slope and y-intercept don't affect how linear functions are used in real life.

Question 29

What is the key difference between a relation and a function?

Accepted Answer

A relation is a set of pairs, while a function is a special type of relation where each input has only one output.

Answer

A function is a set of pairs, while a relation is a special type of function where each input can have multiple outputs.

Answer

A relation is a set of ordered pairs, while a function is a set of unordered pairs.

Answer

A function is a set of ordered pairs, while a relation is a set of unordered pairs.

Question 30

Which of the following describes the relationship between logarithmic and exponential functions?

Accepted Answer

They are inverse functions.

Answer

They share the same domain and range.

Answer

They are both increasing functions.

Question 31

Which of the following is an exponential function?

Accepted Answer

f(x) = 2^x

Answer

f(x) = x^2

Answer

f(x) = -x

Answer

f(x) = 1/x

Question 32

Which of the following is the equation of a function that is decreasing and has a y-intercept of 3?

Accepted Answer

f(x) = -x + 3

Answer

f(x) = x^2 + 3

Answer

f(x) = 2^x + 3

Answer

f(x) = 1/x + 3

Question 33

Which function is an example of a piecewise function?

Accepted Answer

f(x) = |x - 1|

Answer

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

Answer

f(x) = sin(x)

Question 34

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

x < 2

Question 35

What is the range of the function f(x) = -|x|?

Accepted Answer

y ≤ 0

Answer

y ≥ 0

Answer

y > 0

Answer

y < 0

Question 36

Which graph represents the function f(x) = 2^x?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Hyperbola

Question 37

What is the inverse of the function f(x) = 2x + 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 38

Which of the following is a composite function?

Accepted Answer

f(x) = sqrt(x) + 1

Answer

f(x) = x^2

Answer

f(x) = sin(x)

Answer

f(x) = x + 2

Question 39

Find f(f(2)) if f(x) = x - 1?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 40

Which equation represents a rational function?

Accepted Answer

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

Answer

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

Answer

f(x) = e^(x^2)

Answer

f(x) = |x - 5|

Question 41

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 5

Answer

y = x^2 - 4

Answer

y = 2^x

Answer

y = 1/x

Question 42

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 43

Which of the following graphs could represent an exponential function?

Accepted Answer

A curve that increases rapidly

Answer

A straight line

Answer

A parabola

Answer

A circle

Question 44

What is the domain of the function f(x) = √(x + 1)?

Accepted Answer

x ≥ -1

Answer

All real numbers

Answer

x > -1

Answer

x ≤ -1

Question 45

What is the y-intercept of the graph of the function y = -x^2 + 3?

Accepted Answer

3

Answer

0

Answer

1

Answer

2

Question 46

What is the period of the function y = 2cos(3x)?

Accepted Answer

2π/3

Answer

1

Answer

π/3

Answer

π

Question 47

Find a domain and a range of the following function: f(x) = 2x + 1

Accepted Answer

Domain: All real numbers, Range: All real numbers

Answer

Domain: Positive real numbers, Range: Negative real numbers

Answer

Domain: Negative real numbers, Range: All real numbers

Answer

Domain: All real numbers, Range: Positive real numbers

Question 48

Find the slope and y-intercept of the graph of the function f(x) = 3x - 5.

Accepted Answer

Slope: 3, y-intercept: -5

Answer

Slope: -3, y-intercept: 5

Answer

Slope: 5, y-intercept: -3

Answer

Slope: -5, y-intercept: 3

Question 49

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 50

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A circle

Answer

A parabola

Question 51

What is the domain of the function f(x) = 2x + 1?

Accepted Answer

All real numbers

Answer

Negative numbers only

Answer

Positive numbers only

Answer

Integers only

Question 52

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

Accepted Answer

f(x) = ax² + bx + c

Answer

f(x) = mx + b

Answer

f(x) = ex

Question 53

What is the vertex of the parabola represented by the function f(x) = x² - 4x + 3?

Accepted Answer

(2, -1)

Answer

(4, -1)

Answer

(2, 1)

Answer

(0, 3)

Question 54

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

Accepted Answer

A curve that rises steeply to the right

Answer

A parabola

Answer

A straight line

Answer

A circle

Question 55

What is the base of the exponential function f(x) = 3^x?

Accepted Answer

3

Answer

x

Answer

f

Answer

e

Question 56

What is the inverse of the function f(x) = 2x + 1?

Accepted Answer

f⁻¹(x) = (x - 1)/2

Answer

f⁻¹(x) = 2x - 1

Answer

f⁻¹(x) = 1/2x + 1

Answer

f⁻¹(x) = x² + 1

Question 57

Which of the following graphs represents a linear function?

Accepted Answer

A straight line

Answer

A circle

Answer

A parabola

Answer

An ellipse

Question 58

What is the domain of the function f(x) = 1/sqrt(x - 2)?

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 0

Answer

All real numbers

Question 59

Which transformation will move the graph of y = f(x) 2 units down?

Accepted Answer

y = f(x) - 2

Answer

y = 2f(x)

Answer

y = f(x + 2)

Answer

y = f(x) + 2

Question 60

Find the inverse of the function f(x) = 3x + 1.

Accepted Answer

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

Answer

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

Answer

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

Question 61

Which type of function has a constant rate of change?

Accepted Answer

Linear function

Answer

Trigonometric function

Answer

Exponential function

Answer

Quadratic function

Question 62

Determine the domain of the linear function f(x) = 2x + 1.

Accepted Answer

All real numbers

Answer

Natural numbers only

Answer

Integers only

Answer

Positive real numbers only

Question 63

Find the y-intercept of the linear function f(x) = -3x + 5.

Accepted Answer

5

Answer

-5

Answer

-3

Answer

3

Question 64

Identify the correct example of an exponential function from the given options.

Accepted Answer

f(x) = 2^x

Answer

f(x) = 1/x

Answer

f(x) = x^2

Answer

f(x) = sin(x)