A 'V' shape opening downward with vertex at $(0, 2)$

Question 1

Given the function $f(x)$ shown in the graph, determine the intervals on which $f(x)$ is increasing.

Accepted Answer

$(-\infty, -2) \cup (1, 3)$

Question 2

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

Accepted Answer

$A(x) = x(200 - 2x)$

Question 3

Which of the following graphs represents the solution to the system $\begin{cases} x + y = 2 \ x - y = 4 \end{cases}$?

Accepted Answer

The graph where the lines intersect at $(3, -1)$

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

$2x + h - 3$

Question 5

Find all $x$-intercepts of the function $f(x) = x^2 - 4x + 3$.

Accepted Answer

$x = 1$ and $x = 3$

Question 6

Suppose $f(x)$ is an even function. Which of the following statements is true?

Accepted Answer

$f(-x) = f(x)$ for all $x$ in the domain of $f$

Question 7

Given $g(x) = \sqrt{x-1}$, what is the domain of $g$?

Accepted Answer

$[1, \infty)$

Question 8

Which of the following is the correct equation for a parabola that opens downward and has vertex at $(2, 3)$?

Accepted Answer

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

Question 9

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

Accepted Answer

$-2x^3 - x^2 + 5$

Question 10

A sound wave travels at 340 m/s. If its frequency is 850 Hz, what is its wavelength?

Accepted Answer

$0.4$ m

Question 11

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

Accepted Answer

Shift right 3 units, up 2 units

Question 12

If $f(x) = \frac{1}{x}$, which of the following describes the end behavior as $x 	o 0^+$?

Accepted Answer

$f(x) 	o +\infty$

Question 13

Which of the following is the correct difference quotient for $f(x) = x^2$?

Accepted Answer

$2x + h$

Question 14

Given the function $f(x) = \sin(x)$, which of the following statements is true?

Accepted Answer

$f(x)$ is an odd function

Question 15

Which of the following is the correct interval notation for the solution set of $x^2 < 9$?

Accepted Answer

$(-3, 3)$

Question 16

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(x)$?

Accepted Answer

$(f \circ g)(x) = (x+1)^2$

Question 17

Which of the following is the correct graph for $y = -|x| + 2$?

Accepted Answer

A 'V' shape opening downward with vertex at $(0, 2)$

Question 18

If $f(x) = x^3 - 2x^2 + x$, what is the slope of the tangent line at $x = 1$?

Accepted Answer

$0$

Question 19

Suppose $h(x)$ is a function such that $h(x) = h(-x)$ for all $x$. Which of the following must be true?

Accepted Answer

$h(x)$ is even$

College Algebra: Functions, Graphs, and Applications Study Guide

Study Guide - Practice Questions