Q: A function $f$ is increasing on an interval $I$ if:

$f(x_1) < f(x_2)$ whenever $x_1 < x_2$ in $I$

Q: Suppose the graph of $f(x)$ passes the vertical line test. What does this imply?

Each input $x$ has exactly one output $f(x)$, so $f$ is a function.

Q: If $f(x) = 12x^3 + 4x - 3x^2$, which of the following statements is true about its increasing and decreasing intervals?

$f$ is increasing on $(-\infty, -1]$ and $[2, \infty)$, and decreasing on $[-1, 0]$ and $[0, 2]$

Q: A local maximum value of a function $f$ at $x = a$ means:

$f(a) \geq f(x)$ for all $x$ near $a$

Q: Which of the following real-world scenarios is best modeled by a power function?

The area $A$ of a circle as a function of its radius $r$, $A(r) = \pi r^2$

Question 1

Which of the following best describes a function?

Accepted Answer

A rule that assigns to each element $x$ in a set $A$ exactly one element, called $f(x)$, in a set $B$.

Question 2

Which of the following is NOT a valid way to represent a function?

Accepted Answer

Using a random list of numbers with no relationship.

Question 3

A company charges a flat fee of $\$50$ for a service, regardless of the number of hours worked. Which type of function best models this situation?

Accepted Answer

A constant function $f(x) = 50$

Question 4

Given the function $f(x) = 2x + 3$, what is the $y$-intercept of its graph?

Accepted Answer

$3$

Question 5

Which of the following graphs does NOT represent a function?

Accepted Answer

A circle centered at the origin

Question 6

If $f(x) = x^2$ and $g(x) = \sqrt{x}$, which of the following statements is true about their domains?

Accepted Answer

The domain of $f(x)$ is all real numbers, while the domain of $g(x)$ is $[0, \infty)$.

Question 7

A function $f$ is increasing on an interval $I$ if:

Accepted Answer

$f(x_1) < f(x_2)$ whenever $x_1 < x_2$ in $I$

Question 8

Suppose the graph of $f(x)$ passes the vertical line test. What does this imply?

Accepted Answer

Each input $x$ has exactly one output $f(x)$, so $f$ is a function.

Question 9

Given $f(x) = 2x^2 + 3$ and $g(x) = 5x + 6$, for which values of $x$ do the graphs of $f$ and $g$ intersect?

Accepted Answer

$x = -0.5$ and $x = 3$

Question 10

For the function $f(x) = \sqrt{4 - x^2}$, what is the domain?

Accepted Answer

$[-2, 2]$

Question 11

If $f(x) = 12x^3 + 4x - 3x^2$, which of the following statements is true about its increasing and decreasing intervals?

Accepted Answer

$f$ is increasing on $(-\infty, -1]$ and $[2, \infty)$, and decreasing on $[-1, 0]$ and $[0, 2]$

Question 12

A local maximum value of a function $f$ at $x = a$ means:

Accepted Answer

$f(a) \geq f(x)$ for all $x$ near $a$

Question 13

Which of the following real-world scenarios is best modeled by a power function?

Accepted Answer

The area $A$ of a circle as a function of its radius $r$, $A(r) = \pi r^2$

Question 14

If the solution to $f(x) < g(x)$ is the interval $[-0.5, 3]$, what does this mean graphically?

Accepted Answer

The graph of $f(x)$ lies below the graph of $g(x)$ for $x$ in $[-0.5, 3]$

Question 15

Which of the following is a root function?

Accepted Answer

$f(x) = x^{1/2}$

Question 16

A function $f$ is decreasing on an interval $I$ if:

Accepted Answer

$f(x_1) > f(x_2)$ whenever $x_1 < x_2$ in $I$

Question 17

Which of the following best describes the range of the function $f(x) = x^2$?

Accepted Answer

$[0, \infty)$

Question 18

If a function $f$ is defined by the rule 'square the number', which of the following is the correct formula?

Accepted Answer

$f(x) = x^2$

Question 19

A local minimum value of a function $f$ at $x = a$ means:

Accepted Answer

$f(a) \leq f(x)$ for all $x$ near $a$

Functions and Their Graphs: College Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards