Question 1

A ladder is leaning against a building. The base of the ladder is 3 ft from the building, and the ladder is 12 ft long. How tall is the building where the ladder touches it?

Accepted Answer

$\sqrt{12^2 - 3^2} = 11.57$ ft

Question 2

Given the function $f(x) = x^2 - 2$, what is the domain of $f(x)$?

Accepted Answer

$(-\infty, \infty)$

Question 3

Solve the equation $3x^2 + x - 2 = 0$.

Accepted Answer

$x = -2, x = \frac{1}{3}$

Question 4

Find the equation of the circle with center $(-6,4)$ and radius $3$.

Accepted Answer

$(x+6)^2 + (y-4)^2 = 9$

Question 5

Given $f(x) = 3x^2 + 5x$, find $\frac{f(x+h) - f(x)}{h}$.

Accepted Answer

$6x + 5 + 3h$

Question 6

A $\$933$ investment is compounded quarterly at $5\%$ annual interest for $4$ years. What is the future value?

Accepted Answer

$933(1 + \frac{0.05}{4})^{16}$

Question 7

Find the inverse of $f(x) = \sqrt{x-3} + 1$.

Question 8

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

Accepted Answer

$(x-2)^2 - 2$

Question 9

Which of the following functions is odd?

Accepted Answer

$f(x) = x^5 - 5x$

Question 10

Given $f(x) = x^3 - 3x^2 + 5x$, list all possible rational roots.

Accepted Answer

$\pm1, \pm5$

Question 11

Find the domain of $f(x) = \frac{6}{x-4}$.

Accepted Answer

$(-\infty, 4) \cup (4, \infty)$

Question 12

Solve the inequality $-8x + 9 < 6$.

Accepted Answer

$x > \frac{3}{8}$

Question 13

Given $y = x^2 - 2x - 8$, find the vertex.

Accepted Answer

$(1, -9)$

Question 14

Find the equation of the line in slope-intercept form passing through $(3,5)$ and $(4,9)$.

Accepted Answer

$y = 4x - 7$

Question 15

Expand $\log_x y - 3 \log_x z$ using logarithm properties.

Accepted Answer

$\log_x \frac{y}{z^3}$

Question 16

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

Accepted Answer

$x^2 - x$

Question 17

Find the solution to the system: $x + 4y + z = 2$, $x - 3y - z = -24$, $x + y + z = -11$.

Accepted Answer

$(2,1,-3)$

Question 18

Given $f(x) = \frac{1}{x-3} + 4$, find the $y$-intercept.

Accepted Answer

$(0, \frac{1}{-3} + 4)$

Question 19

Given $P(t) = 386000e^{-0.036t}$, how long will it take for the population to reach $60,000$?

Accepted Answer

$t = \frac{\ln(60,000/386,000)}{-0.036}$

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards