$\begin{bmatrix} 12 & 7 \\ 19 & 11 \end{bmatrix}$

As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to \infty$

Question 1

Solve for $x$ over the complex numbers: $2x^2 - 5x = -3$.

Accepted Answer

$x = 1, x = 1.5$

Question 2

Which of the following is the solution to $\log_2(x+2) + \log_2(x-1) = 1$?

Accepted Answer

$x = 3$

Question 3

Find the equation of the line perpendicular to $y = 4x + 69$ that passes through $(7, 5)$.

Accepted Answer

$y = -\frac{1}{4}x + \frac{33}{4}$

Question 4

Solve the inequality and write the solution in interval notation: $|2x - 3| \leq 11$.

Accepted Answer

$[-4, 7]$

Question 5

Given the function $f(x) = \frac{2x^2 - 5x + 3}{x - 1}$, find the $y$-intercept.

Accepted Answer

$(0, 3)$

Question 6

A population of bacteria starts at 1,000 and grows at a rate of 5% compounded quarterly. Which equation models the population after $t$ years?

Accepted Answer

$P = 1000(1 + 0.05/4)^{4t}$

Question 7

Find the determinant of the matrix $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$.

Accepted Answer

$-10$

Question 8

Expand the logarithmic expression: $\log\left(\frac{x^2y}{z^3}\right)$.

Accepted Answer

$2\log x + \log y - 3\log z$

Question 9

Given the quadratic $y = x^2 + 2x + 3$, what is the vertex of the parabola?

Question 10

Find the domain of the function $f(x) = \frac{2x}{x^2 - 9}$.

Accepted Answer

$x 
eq -3, x 
eq 3$

Question 11

If $\log_2(x) + \log_2(x-3) = 3$, what is the value of $x$?

Accepted Answer

$x = 8$

Question 12

Which of the following is the equation of the circle with center $(4, -6)$ and radius $8$?

Accepted Answer

$(x - 4)^2 + (y + 6)^2 = 64$

Question 13

Find the sum $\sum_{k=1}^{4} (k^2 - 3)$.

Accepted Answer

$24$

Question 14

Given $f(x) = x^2 - 2x + 5$, what is the axis of symmetry?

Accepted Answer

$x = 1$

Question 15

Which of the following is the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{x^2 - 1}$?

Accepted Answer

$y = 3$

Question 16

If $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \ 5 & 3 \end{bmatrix}$, what is $AB$?

Accepted Answer

$\begin{bmatrix} 12 & 7 \ 19 & 11 \end{bmatrix}$

Question 17

Find and simplify the difference quotient $\frac{f(x+h) - f(x)}{h}$ for $f(x) = x^2 - 4x$.

Accepted Answer

$2x + h - 4$

Question 18

Given the function $f(x) = \frac{x^2 - 2x + 5}{x - 1}$, find $f(1)$.

Accepted Answer

Undefined

Question 19

Which of the following best describes the end behavior of $f(x) = -2x^3 + 5x^2 - x + 7$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o \infty$

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions