Question 1

Which of the following best describes the domain and range of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 2

Which function has a graph that passes through the origin and is symmetric with respect to the origin?

Accepted Answer

Cube function $$f(x) = x^3$

Question 3

A medical researcher models the growth of bacteria with the function $$f(x) = x^2$. If x$ represents time in hours, what is the range of possible bacteria counts?

Accepted Answer

$$[0, \infty)$$

Question 4

Which of the following functions is NOT one-to-one?

Accepted Answer

Square function $$f(x) = x^2$

Question 5

Suppose a company’s profit is modeled by the function $$f(x) = 5$$, where $$x is $$the number of products sold. What does this imply about the company’s profit?

Accepted Answer

Profit remains constant regardless of sales.

Question 6

Which function’s graph is always increasing for all real numbers $$x$$?

Accepted Answer

Cube function $$f(x) = x^3$

Question 7

If $$f(x) = \sqrt[3]{x}$$, what is $$f(-8)$$?

Accepted Answer

$$-2$$

Question 8

Which of the following statements is true about the identity function $$f(x) = x$$?

Accepted Answer

Its graph is a straight line passing through the origin with slope 1.

Question 9

A physicist uses the function $$f(x) = x^3$ to model the volume of a cube with side length x$. What is the domain of this function in this context?

Accepted Answer

$$[0, \infty)$$

Question 10

Which function has a range of all real numbers but a restricted domain?

Accepted Answer

Square root function $$f(x) = \sqrt{x}$$

Question 11

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the composition f(g(x$$))$$?

Accepted Answer

$$x$$

Question 12

Which function is even?

Accepted Answer

Square function $$f(x) = x^2$

Question 13

A biologist models the population of a species with $$f(x) = \sqrt{x}$$, where $$x is $$the number of years since introduction. What is the minimum possible population according to this model?

Accepted Answer

$$0$$

Question 14

Which function is odd?

Accepted Answer

Cube function $$f(x) = x^3$

Question 15

If $$f(x) = x^2$ and x$ is replaced by -x$, what is f(-x$$)$$?

Accepted Answer

$$x^2$$

Question 16

Which function’s graph is a horizontal line?

Accepted Answer

Constant function $$f(x) = c$$

Graphs of Common Functions: Key Types and Properties

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