Question 1

Which of the following systems of equations has exactly one solution, and what is that solution?

$\begin{cases} y = 4x - 3 \ 2y + 10x = 48 \end{cases}$

Accepted Answer

Exactly one solution: $x = 3$, $y = 9$

Question 2

Given the relation $\{(4, 9), (2, 7), (4, -5), (5, -7)\}$, what is the domain and is this relation a function?

Accepted Answer

Domain: $\{2, 4, 5\}$; No, it is not a function because $x=4$ maps to two different $y$ values.

Question 3

Which of the following equations defines $y$ as a function of $x$?

Accepted Answer

$y = x^3 - 64$

Question 4

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

Accepted Answer

$\dfrac{\sqrt{8} - \sqrt{2}}{8 - 2}$

Question 5

Given the function $f(x) = 5x + 1$, what is its inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \dfrac{x - 1}{5}$

Question 6

What is the standard form of the equation of a circle with center $(-2, 9)$ and radius $10$?

Accepted Answer

$(x + 2)^2 + (y - 9)^2 = 100$

Question 7

Given $f(x) = x^2 + 5x$ from $x_1 = 4$ to $x_2 = 6$, what is the average rate of change?

Accepted Answer

$\dfrac{f(6) - f(4)}{6 - 4}$

Question 8

Which of the following describes the transformation needed to graph $g(x) = |x - 2| + 4$ from $f(x) = |x|$?

Accepted Answer

Shift right 2 units, shift up 4 units.

Question 9

Find the zeros of $f(x) = 3x^4 + 4x - x^3$ and state the multiplicity of each zero.

Question 10

Which of the following is the correct condensed form of $\log_3 15 - \log_3 5$?

Accepted Answer

$\log_3 3$

Question 11

If $A = P\left(1 + \dfrac{r}{n}\right)^{nt}$, what is the accumulated value of an investment of $\$1,500$ for $2$ years at an interest rate of $8\%$ compounded quarterly?

Accepted Answer

$A = 1500\left(1 + \dfrac{0.08}{4}\right)^{8}$

Question 12

Which of the following is the correct logarithmic form of $5^3 = 125$?

Accepted Answer

$\log_5 125 = 3$

Question 13

Given $f(x) = \dfrac{2x}{x^2 - 9}$, what are the vertical asymptotes?

Accepted Answer

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

Question 14

Solve the equation $2^{(x - 7)} = 4$ for $x$.

Accepted Answer

$x = 9$

Question 15

What is the domain of $f(x) = \sqrt{x - 5}$?

Accepted Answer

$x \geq 5$

Question 16

Which of the following is the correct expansion of $\log_2 \left(\dfrac{\sqrt{8}}{5}\right)$ using properties of logarithms?

Accepted Answer

$\dfrac{1}{2} \log_2 8 - \log_2 5$

Question 17

Given the quadratic function $f(x) = x^2 + 2x - 8$, what is the axis of symmetry?

Accepted Answer

$x = -2$

Question 18

If $f(x) = 3x^3 + 2x^2 - 5x - 6$, use the Rational Zero Theorem to list all possible rational zeros.

Accepted Answer

$\pm1, \pm2, \pm3, \pm6, \pm\dfrac{1}{3}, \pm\dfrac{2}{3}, \pm\dfrac{3}{3}, \pm\dfrac{6}{3}$

Question 19

Which of the following is the correct exponential form of $\log_4 256 = x$?

Accepted Answer

$4^x = 256$

Precalculus Final Exam Review: Key Concepts and Practice Problems

Study Guide - Practice Questions

Study Guide - Flashcards