Question 1

Given the function $f(x) = x^3 - 3x^2 - 9x + 5$, determine the intervals on which the function is increasing.

Accepted Answer

$(-\infty, 0) \cup (3, \infty)$

Question 2

A farmer has 200 ft of fencing to enclose a rectangular area. If the enclosed area is $A$ and the length is $x$, express $A$ as a function of $x$.

Accepted Answer

$A(x) = x(100 - x)$

Question 3

Which of the following is the correct graph for the system of equations $\begin{cases} y = 2x - 1 \ y = -x + 2 \end{cases}$?

Accepted Answer

Graph A: Lines intersect at $(1, 1)$

Question 4

For the function $f(x) = x^2 - 3x + 2$, construct and simplify the difference quotient $\frac{f(x+h) - f(x)}{h}$.

Accepted Answer

$2x - 3 + h$

Question 5

Given $f(x) = \sqrt{x - 1}$, find the domain of $f$.

Accepted Answer

$x \geq 1$

Question 6

Find all $x$ such that $f(x) = 0$ for $f(x) = x^2 - 4x + 3$.

Accepted Answer

$x = 1$ and $x = 3$

Question 7

Suppose the point $P$ is symmetric to the point $(2, 3)$ with respect to the $y$-axis. What are the coordinates of $P$?

Accepted Answer

$(-2, 3)$

Question 8

Which of the following equations represents a parabola that opens downward and has vertex at $(0, 4)$?

Accepted Answer

$y = -x^2 + 4$

Question 9

If $f(x) = 2x^2 - 5x + 3$, what is $f(4)$?

Question 10

Given $f(x) = x^2$ and $g(x) = x + 1$, find $(f \circ g)(2)$.

Accepted Answer

$9$

Question 11

Which of the following describes the transformation of the graph of $y = x^2$ to $y = (x - 3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 12

Which of the following is the correct interval notation for the solution to $|x - 2| < 5$?

Accepted Answer

$(-3, 7)$

Question 13

If $f(x) = \sin(x)$, which of the following statements is true about its period?

Accepted Answer

The period is $2\pi$

Question 14

Which of the following is the correct equation for a line passing through $(0, 2)$ with slope $-3$?

Accepted Answer

$y = -3x + 2$

Question 15

Given $f(x) = x^2 - 4$, which of the following describes the symmetry of the function?

Accepted Answer

Even

Question 16

If $f(x) = 2x + 1$ and $g(x) = x^2$, find $(f \circ g)(3)$.

Accepted Answer

$19$

Question 17

Which of the following is the correct solution to $2x^2 - 8 = 0$?

Accepted Answer

$x = 2$ and $x = -2$

Question 18

A sound wave travels at 340 m/s and has a frequency of 850 Hz. What is its wavelength?

Accepted Answer

$0.4$ m

Question 19

Which of the following is the correct equation for a function whose graph is that of $y = x^2$ but shifted left 5 units and down 3 units?

Accepted Answer

$y = (x + 5)^2 - 3$

Question 20

If $f(x) = x^2$ and $g(x) = 2x$, what is $(f + g)(3)$?

Accepted Answer

$15$

College Algebra: Functions, Graphs, and Applications Study Guide

Study Guide - Practice Questions