Operations with Functions and Graphical Analysis Quiz

Test your understanding of functions with questions on domains, ranges, inverses, intercepts, rates of change, and more.

Practice Learn Test

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

(-∞, -3]

(-3, ∞)

(-∞, 0]

[0, ∞)

What is the range of the function g(x) = 2x^2 - 5x + 3?

(-∞, 3]

[3, ∞)

(-∞, 0]

[0, ∞)

What is the inverse of the function h(x) = 4x - 7?

h^(-1)(x) = (x + 7) / 4

h^(-1)(x) = (x - 7) / 4

h^(-1)(x) = (x / 4) - 7

h^(-1)(x) = (x - 7) * 4

Which of the following functions is odd?

f(x) = x^3 - x

f(x) = x^2 + x

f(x) = x^4 - 3x^2

f(x) = x^2 - 2

Which of the following functions is even?

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

f(x) = x^3 - x

f(x) = x^2 + x

f(x) = x^2 - 3

What is the average rate of change of the function f(x) = 2x^2 - 3x over the interval [1, 3]?

-1

-7

What is the maximum or minimum value of the function f(x) = x^2 - 4x + 3?

Maximum value: 3

Minimum value: 1

Maximum value: 1

Minimum value: 3

Which of the following functions is neither even nor odd?

f(x) = x^5

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

f(x) = sin(x)

f(x) = e^x

What are the x-intercepts of the function y = (x - 2)(x + 3)?

{-3, 2}

{-2, 3}

{2, -3}

{3, -2}

#10

Which of the following statements about even functions is true?

Even functions are symmetric about the x-axis.

Even functions are symmetric about the y-axis.

Even functions have odd exponents in their terms.

Even functions have a period of π.

#11

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

(-∞, 0) ∪ (0, ∞)

(-∞, -1] ∪ [1, ∞)

(-1, 1)

(-1, 0) ∪ (0, 1)

#12

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

#13

For the function f(x) = |x|, what is f(-3)?

-3

-1

#14

What are the critical points of the function f(x) = x^3 - 6x^2 + 9x?

{0, 2, 3}

{0, 2}

{0, 3}

{2, 3}