Question 1

Evaluate $(fg)(-2)$ for $f(x) = x + 1$ and $g(x) = 2x^2 + 15x + 6$. What is the value?

Accepted Answer

$16$

Question 2

Complete the square for $x^2 - 6x + 9 + y^2 + 6y + 9 = 36$ and write the equation in standard form. What are the center and radius of the circle?

Accepted Answer

$(x - 3)^2 + (y + 3)^2 = 36$; Center: $(3, -3)$, Radius: $6$

Question 3

For $f(x) = -5x + 9$ and $g(x) = 2x + 3$, find $(g \circ f)(x)$.

Accepted Answer

$-10x + 21$

Question 4

Given $f(x) = \frac{x - 5}{7}$ and $g(x) = 7x + 5$, what is $(g \circ f)(x)$?

Accepted Answer

$x$

Question 5

Find $(g \circ f)(20)$ for $f(x) = \frac{x - 2}{6}$ and $g(x) = 4x + 9$.

Accepted Answer

$21$

Question 6

Which two functions are inverses of each other? $f(x) = 9x$, $g(x) = \frac{x}{9}$, $h(x) = \frac{9}{x}$

Accepted Answer

f(x) and g(x)

Question 7

Find the midpoint of the line segment with endpoints $\left(-\frac{8}{3}, -\frac{7}{5}\right)$ and $\left(\frac{7}{3}, -\frac{9}{5}\right)$.

Accepted Answer

$\left(-\frac{1}{6}, -\frac{8}{5}\right)$

Question 8

Write the standard form of the equation of the circle with center $(-5, -4)$ and radius $19$.

Accepted Answer

$(x + 5)^2 + (y + 4)^2 = 19$

Question 9

Find the domain of the composite function $f \circ g$ where $f(x) = \frac{4}{x + 7}$ and $g(x) = x + 3$.

Accepted Answer

$(-\infty, -10) \cup (-10, \infty)$

Question 10

Find the inverse of the function $f(x) = \frac{3x - 4}{5}$.

Accepted Answer

$f^{-1}(x) = \frac{5x + 4}{3}$

Question 11

Describe how the graph of $f(x) = (x - 2)^2 + 4$ relates to the graph of $y = x^2$.

Accepted Answer

A translation 2 units to the right and 4 units up

Question 12

Find the domain of $h(x) = \frac{x - 2}{x^3 - 4x}$.

Accepted Answer

$(-\infty, -2) \cup (-2, 0) \cup (0, 2) \cup (2, \infty)$

Question 13

Given $f(x) = 2 - 5x$ and $g(x) = -7x^2 + 5$, find $(f + g)(x)$.

Accepted Answer

$-7x^2 - 5x + 7$

Question 14

Find the distance between the points $(-\frac{4}{7}, -2)$ and $(-\frac{3}{7}, 1)$.

Accepted Answer

$4$

Question 15

Find the average rate of change of $f(x) = 5x + 7$ from $x_1 = -1$ to $x_2 = 0$.

Accepted Answer

$5$

Question 16

Write the equation of the line passing through $(3, 5)$ and perpendicular to $-4x + y - 6 = 0$ in slope-intercept form.

Accepted Answer

$y = -\frac{1}{4}x + \frac{23}{4}$

Question 17

Find the slope of the line passing through $(-3, 3)$ and $(-2, 3)$.

Accepted Answer

$0$

Question 18

Find the average rate of change of $f(x) = 2x$ from $x_1 = 2$ to $x_2 = 8$.

Accepted Answer

$\frac{1}{3}$

College Algebra Test #2 Review – Step-by-Step Guidance

Study Guide - Practice Questions