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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