Functions: Interactive Learning Quizzes for Seventh Grade Math

Question 1

Consider the following table:

x | y 
 --|-- 
 1 | 5 
 2 | 7 
 3 | 9

What is the equation of the linear function represented by the table?

Accepted Answer

y = 2x + 3

Answer

y = 3x - 1

Answer

y = x + 4

Answer

y = 2x - 1

Question 2

Consider the function f(x) = x^2 - 4. What is the inverse of this function?

Accepted Answer

f^-1(x) = sqrt(x + 4)

Answer

f^-1(x) = x^2 - 4

Answer

f^-1(x) = -x^2 + 4

Answer

f^-1(x) does not exist

Question 3

Consider the functions f(x) = x - 1 and g(x) = 2x + 3. What is (f - g)(x)?

Accepted Answer

-x + 4

Answer

-x - 4

Answer

x - 4

Answer

x + 4

Question 4

Which of the following functions is a rational function?

Accepted Answer

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

Answer

f(x) = 2^(x)

Answer

f(x) = sin(x)

Answer

f(x) = |x|

Question 5

Consider the function f(x) = 2/(x - 3). What is the vertical asymptote of this function?

Accepted Answer

x = 3

Answer

x = 0

Answer

x = 2

Answer

x = -3

Question 6

Which function is shown by a straight line that goes through the point (0,0)?

Accepted Answer

Linear function

Answer

Exponential function

Answer

Quadratic function

Question 7

Which of the following equations represents a linear function?

Accepted Answer

y = x + 2

Answer

y = x^2

Answer

y = 1/x

Question 8

How can you determine the range of a function from its graph?

Accepted Answer

Find the highest and lowest output values

Answer

Find the highest and lowest input values

Answer

Calculate the slope of the line

Question 9

What is the slope of the linear function y = 2x - 3?

Accepted Answer

2

Answer

-3

Answer

1

Question 10

Which of the following is NOT a characteristic of a function?

Accepted Answer

The input and output are always the same

Answer

Each input corresponds to exactly one output

Answer

The output changes based on the input

Question 11

Which type of graph represents a constant function?

Accepted Answer

Horizontal line

Answer

Vertical line

Answer

Parabola

Question 12

Which of the following graphs accurately represents the function f(x) = x^2?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Question 13

Which of the following equations represents the function that is a horizontal line passing through the point (2, 5)?

Accepted Answer

y = 5

Answer

y = 2

Answer

x = 2

Answer

x = 5

Question 14

For the function f(x) = -x^2, what is the range of y?

Accepted Answer

All non-positive real numbers

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 15

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 16

Given the functions f(x) = x^2 and g(x) = x + 2, what is the composition f(g(x))?

Accepted Answer

f(g(x)) = x^2 + 4x + 4

Answer

f(g(x)) = x^2 + 2

Answer

g(f(x)) = x^4 + 2

Answer

g(f(x)) = x^4 + 4x^2 + 4

Question 17

Consider the function f(x) = 2x + 3. What is the value of f(-1)?

Accepted Answer

-5

Answer

1

Answer

5

Answer

7

Question 18

If f(x) and g(x) are functions, what does f(g(x)) represent?

Accepted Answer

The output of g(x) plugged into f(x)

Answer

The output of f(x) plugged into g(x)

Answer

The sum of f(x) and g(x)

Answer

The difference between f(x) and g(x)

Question 19

Consider the function f(x) = x^2 - 1. What is the inverse of this function?

Accepted Answer

g(x) = √(x - 1)

Answer

g(x) = x^2 + 1

Answer

g(x) = √(x + 1)

Answer

g(x) = -x^2 - 1

Question 20

Which of the following equations represents a quadratic function?

Accepted Answer

y = x^2 - 4

Answer

y = 2x + 3

Answer

y = √x

Answer

y = 1/x

Question 21

Consider the function f(x) = 3x - 2. What is the slope of this function?

Accepted Answer

3

Answer

2

Answer

-2

Answer

-3

Question 22

Consider the function f(x) = x^3 - 8. What is the y-intercept of this function?

Accepted Answer

-8

Answer

0

Answer

8

Answer

1

Question 23

Which of the following is a characteristic of a function?

Accepted Answer

Each input value corresponds to exactly one output value.

Answer

The output value can repeat for different input values.

Answer

The input value can repeat for different output values.

Answer

The output value is always greater than the input value.

Question 24

In the function f(x) = ax + b, identify the independent and dependent variables.

Accepted Answer

Independent: x, Dependent: f(x)

Answer

Independent: f(x), Dependent: x

Answer

Independent: a, Dependent: b

Answer

Independent: b, Dependent: a

Question 25

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 26

Write the equation of the line that passes through the point (3, 2) and has a slope of -2.

Accepted Answer

y = -2x + 8

Answer

y = 2x - 4

Answer

y = -x + 5

Answer

y = x + 1

Question 27

What transformation translates the graph of the function f(x) = x^2 left by 3 units?

Accepted Answer

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

Answer

g(x) = (x + 3)^2

Answer

g(x) = x^2 + 3

Answer

g(x) = x^2 - 3

Question 28

A rectangular garden has a perimeter of 50 feet. What dimensions maximize the garden's area?

Accepted Answer

Length: 12.5 feet, Width: 12.5 feet

Answer

Length: 25 feet, Width: 12.5 feet

Answer

Length: 10 feet, Width: 20 feet

Answer

Length: 15 feet, Width: 15 feet

Question 29

Which of the following describes a function?

Accepted Answer

A set of ordered pairs where each first coordinate is related to exactly one second coordinate

Answer

A set of ordered pairs where each second coordinate is related to exactly one first coordinate

Answer

A set of ordered pairs with no repeating first or second coordinates

Answer

A graph where all points lie on a line

Question 30

The domain of a function refers to the set of:

Accepted Answer

Input values

Answer

Output values

Answer

All values on the x-axis

Answer

All values on the y-axis

Question 31

The graph of a function is a parabola that opens upward. What is the range of the function?

Accepted Answer

All real numbers greater than or equal to the vertex

Answer

All real numbers less than the vertex

Answer

All real numbers

Answer

Cannot be determined from the given information

Question 32

Consider the function f(x) = 2x + 1. What is the y-intercept of the graph of this function?

Accepted Answer

1

Answer

-2

Answer

2

Answer

3

Question 33

Which of the following is the inverse of the function f(x) = (x - 2)^2?

Accepted Answer

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

Answer

f^-1(x) = 1/x

Answer

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

Answer

The function has no inverse

Question 34

The graph of the function g(x) = |x - 1| is shown below. What is the domain of this function?

Accepted Answer

All real numbers

Answer

All non-negative real numbers

Answer

All positive real numbers

Answer

All integers

Question 35

A function f(x) is transformed to create a new function g(x) = -f(x + 2). What is the effect of this transformation?

Accepted Answer

The graph of g(x) is shifted 2 units left and reflected across the x-axis.

Answer

The graph of g(x) is shifted 2 units right and reflected across the y-axis.

Answer

The graph of g(x) is stretched vertically by a factor of 2 and shifted 2 units right.

Answer

The graph of g(x) is shrunk horizontally by a factor of 2 and shifted 2 units up.

Question 36

A function f(x) is not one-to-one. Why can't its inverse, f^-1(x), also be a function?

Accepted Answer

A function requires each input to have a unique output, which f(x) doesn't.

Answer

The inverse of a function is always a function, regardless of whether the original function is one-to-one.

Answer

A one-to-many function like f(x) can have an inverse that is one-to-one.

Question 37

Which relation is not a function? Provide a specific example to support your answer.

Accepted Answer

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

Answer

{(1, 2), (3, 4), (5, 6)}

Answer

{(-1, 0), (0, 1), (1, 1)}

Answer

{(0, 0), (1, 1), (2, 4), (3, 9)}

Question 38

Given the functions f(x) = x^2 and g(x) = 2x - 1, what is (f - g)(x)?

Accepted Answer

x^2 - 2x + 1

Answer

x^2 + 2x - 1

Answer

2x^2 - 1

Answer

-x^2 - 2x + 1

Question 39

What is the range of values for y in the function f(x) = x^2 - 1?

Accepted Answer

y ≥ -1

Answer

All real numbers

Answer

y > 0

Answer

y ≤ -1

Question 40

Which of the following graphs shows a linear function?

Accepted Answer

A straight line

Answer

A parabola

Answer

An exponential curve

Answer

A circle

Question 41

What is the y-intercept of the function f(x) = 3x - 2?

Accepted Answer

-2

Answer

3

Answer

0

Answer

2

Question 42

Find the equation of the function that passes through the points (2, 3) and (4, 7).

Accepted Answer

f(x) = 2x + 1

Answer

f(x) = x^2 - 1

Answer

f(x) = 2x - 1

Answer

f(x) = x^2 + 1

Question 43

What are the numbers that cannot be in the domain of the function f(x) = 1 / (x - 2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

Only positive real numbers

Question 44

What is the slope of the function f(x) = -3x + 2?

Accepted Answer

-3

Answer

-2

Answer

2

Answer

3

Question 45

Which of the following functions is increasing?

Accepted Answer

f(x) = 2x

Answer

f(x) = x^2

Answer

f(x) = -x

Answer

f(x) = 1 / x

Question 46

Which of the following is not a way to represent a function?

Accepted Answer

Story

Answer

Table

Answer

Equation

Answer

Graph

Question 47

Which of the following graphs represents the function f(x) = x^2 + 2?

Accepted Answer

A parabola opening upward

Answer

A circle

Answer

A hyperbola

Answer

A line with a positive slope

Question 48

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

Accepted Answer

All real numbers except 2

Answer

All positive real numbers

Answer

All real numbers

Answer

All negative real numbers

Question 49

Which of the following is the inverse of the function f(x) = 2x + 3?

Accepted Answer

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

Answer

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

Answer

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

Answer

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