Functions and Graphs: Master the Basics with Engaging Quizzes

Question 1

Which of the following accurately represents the graph of a quadratic function with a positive leading coefficient?

Accepted Answer

U-shaped

Answer

Inverted U-shaped

Answer

Linear

Answer

Exponential

Question 2

Which function exhibits a constant rate of change?

Accepted Answer

y = x + 2

Answer

y = x^2

Answer

y = e^x

Answer

y = sin(x)

Question 3

Which transformation will shift a graph 3 units to the left?

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(3x)

Answer

f(x/3)

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

Which transformation will shift the graph of y = x² to the left 2 units?

Accepted Answer

y = (x - 2)².

Answer

y = (x + 2)².

Answer

y = x² - 2.

Answer

y = x² + 2.

Question 6

What is the domain of f(x) = 1/(x - 3)?

Accepted Answer

All real numbers except 3.

Answer

All real numbers.

Answer

All real numbers greater than 3.

Answer

All real numbers less than 3.

Question 7

Which graph represents a function that is both odd and increasing?

Accepted Answer

A straight line with a positive slope.

Answer

A parabola opening upward.

Answer

A parabola opening downward.

Answer

A circle.

Question 8

Which of the following is a trigonometric function?

Accepted Answer

Sine.

Answer

Exponential.

Answer

Logarithmic.

Answer

Quadratic.

Question 9

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

Accepted Answer

All real numbers greater than or equal to zero.

Answer

All real numbers.

Answer

All positive real numbers.

Answer

All negative real numbers.

Question 10

Which of the following is the equation of a linear function with slope m and y-intercept b?

Accepted Answer

y = mx + b

Answer

y = x^2

Answer

y = sin(x)

Answer

y = 1/x

Question 11

Determine the slope of the line represented by the equation y = 3x - 5.

Accepted Answer

3

Answer

5

Answer

-3

Answer

-5

Question 12

For the function f(x) = sqrt(x), what is the domain (the set of valid inputs) of the function?

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All negative real numbers

Answer

Only the number 0

Question 13

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

Accepted Answer

f^-1(x) = x - 3

Answer

f^-1(x) = 3 - x

Answer

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

Answer

f^-1(x) does not exist

Question 14

Identify the type of graph for a sinusoidal function.

Accepted Answer

A wave

Answer

A straight line

Answer

A circle

Answer

A parabola

Question 15

Which of the following equations represents the graph of a linear function?

Accepted Answer

y = 3x + 2

Answer

y = x^2 + 2

Answer

y = sin(x)

Answer

y = x^3 + 1

Question 16

Which of the following is the y-intercept of the function f(x) = -2x + 5?

Accepted Answer

5

Answer

-2

Answer

0

Answer

10

Question 17

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

Accepted Answer

A parabolic shape

Answer

A linear graph

Answer

A V-shaped graph

Answer

An odd degree polynomial

Question 18

What is the vertex of the parabola f(x) = -x^2 + 6x - 5?

Accepted Answer

(3, 4)

Answer

(3, -4)

Answer

(-3, -4)

Answer

(-3, 4)

Question 19

What is the range of the function f(x) = |x + 2|?

Accepted Answer

y ≥ 2

Answer

y ≤ 2

Answer

y > 2

Answer

y < 2

Question 20

Find the domain of the function f(x) = √(x - 5).

Accepted Answer

[5, ∞)

Answer

(-∞, ∞)

Answer

(-∞, 5]

Answer

[0, ∞)

Question 21

What is the equation of the vertical asymptote of the graph of the function f(x) = (x + 1)/(x - 4)?

Accepted Answer

x = 4

Answer

x = 1

Answer

y = 1

Answer

y = 4

Question 22

The function f(x) = 3^x - 4 represents what type of growth?

Accepted Answer

Exponential growth

Answer

Linear growth

Answer

Quadratic growth

Answer

Cubic growth

Question 23

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

Accepted Answer

{x | x ≠ 2}

Answer

{x | x > 2}

Answer

{x | x < 2}

Answer

{x | x ∈ R}

Question 24

Which of the following transformations shifts a function f(x) up by 3 units?

Accepted Answer

f(x) + 3

Answer

f(x - 3)

Answer

f(x) / 3

Answer

f(3x)

Question 25

What is the y-intercept of the function f(x) = -3x + 5?

Accepted Answer

5

Answer

-3

Answer

0

Answer

1

Question 26

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

Accepted Answer

x = 1

Answer

x = 0

Answer

y = 0

Answer

y = 1

Question 27

Which of the following is **not** a key feature of a function?

Accepted Answer

Equation of the graph

Answer

Domain

Answer

Range

Answer

Average rate of change

Question 28

Find the domain of the function: f(x) = √(x + 5)

Accepted Answer

(5, ∞)

Answer

[-5, ∞)

Answer

(-∞, 5]

Answer

(-∞, -5)

Question 29

Identify the type of function represented by the equation: y = 2x² - 5

Accepted Answer

Quadratic

Answer

Linear

Answer

Exponential

Answer

Logarithmic

Question 30

Find the average rate of change of the function: f(x) = x³ - 2x² + 5 over the interval [-1, 2].

Accepted Answer

3

Answer

-3

Answer

1

Answer

5

Question 31

Consider the function: f(x) = 2x - 5. Find the inverse function of f(x).

Accepted Answer

f⁻¹(x) = (x + 5)/2

Answer

f⁻¹(x) = (x - 5)/2

Answer

f⁻¹(x) = 5 - 2x

Answer

f⁻¹(x) = 2 - 5x

Question 32

Which of the following is NOT a key feature of a function?

Accepted Answer

Average value

Answer

Domain

Answer

Range

Question 33

The graph of the function f(x) = x^2 - 4 opens:

Accepted Answer

Upward

Answer

Right

Answer

Downward

Answer

Left

Question 34

Which of the following functions is a linear function?

Accepted Answer

f(x) = 2x + 5

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Answer

f(x) = x^2 - 4

Question 35

The graph of the function f(x) = |x| has the following shape:

Accepted Answer

V-shaped

Answer

U-shaped

Answer

Parabolic

Answer

Exponential

Question 36

The domain of the function f(x) = sqrt(x - 1) is:

Accepted Answer

x ≥ 1

Answer

x < 1

Answer

x ≤ 1

Answer

x > 1

Question 37

The range of the function f(x) = 2cos(x) is:

Accepted Answer

[-2, 2]

Answer

[0, 2π]

Answer

[-1, 1]

Answer

[-2π, 2π]

Question 38

The inverse of the function f(x) = x + 5 is:

Accepted Answer

f^-1(x) = x - 5

Answer

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

Answer

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

Answer

f^-1(x) = x + 5

Question 39

Which of the following is a composite function of f(x) = x^2 and g(x) = x - 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

The average rate of change of the function f(x) = 2x^2 - 3x + 4 over the interval [1, 3] is:

Accepted Answer

8

Answer

12

Answer

6

Answer

10

Question 41

Which of the following is the equation of the line perpendicular to the graph of the function f(x) = -2x + 5 at the point (2, 1)?

Accepted Answer

y = (1/2)x + 2

Answer

y = -2x + 7

Answer

y = -2x + 3

Answer

y = (1/2)x + 3

Question 42

Which of the following equations represents a linear function?

Accepted Answer

y = 3x - 2

Answer

y = x^2 + 1

Answer

y = sin(x)

Answer

y = 1/x

Question 43

What is the domain of the function f(x) = √(x - 3)?

Accepted Answer

x ≥ 3

Answer

All real numbers

Answer

x ≤ 3

Answer

x < 3

Question 44

Which of the following graphs represents a function that is both one-to-one and onto?

Accepted Answer

A straight line passing through the origin with a positive slope

Answer

A horizontal line

Answer

A circle

Answer

A parabola opening upwards

Question 45

What is the inverse of the function 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) = 1 / (2x + 3)

Question 46

Which of the following is an application of linear functions in the real world?

Accepted Answer

Modeling the cost of renting a car (based on mileage)

Answer

Modeling the shape of a circle

Answer

Modeling the growth of a population (exponential growth)

Answer

Modeling the trajectory of a projectile (parabolic path)

Question 47

What is the x-coordinate of the vertex of the parabola y = x² - 4x + 3?

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 48

Which of the following is the graph of the function f(x) = 2x + 1?

Accepted Answer

A straight line with a slope of 2 and a y-intercept of 1

Answer

A horizontal line passing through (0, 1)

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 49

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

Accepted Answer

-3

Answer

-2

Answer

3

Answer

2

Question 50

Which of the following is the y-intercept of the graph of the function h(x) = 2x - 5?

Accepted Answer

-5

Answer

5

Answer

0

Answer

2

Question 51

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

Accepted Answer

All real numbers except 2

Answer

All integers

Answer

All real numbers

Answer

All positive numbers

Question 52

Which of the following is the range of the function g(x) = 3x^2 + 1?

Accepted Answer

All real numbers greater than or equal to 1

Answer

All positive numbers

Answer

All real numbers

Answer

All negative numbers

Question 53

Which of the following is the equation of the line that passes through the points (1,3) and (4,7)?

Accepted Answer

y = x + 2

Answer

y = -x + 5

Answer

y = 2x + 1

Answer

y = x - 1

Question 54

What is the vertex of the parabola represented by the equation f(x) = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(-2, -1)

Answer

(2, 1)