$\log_a \left( \frac{\sqrt{x} y^4}{z^3} \right)$

Question 1

Solve for $x$ in the equation $2x^2 - 3x + 1 = 0$.

Accepted Answer

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

Question 2

Which of the following is the equation of the circle with center $(4, 4)$ and radius $3$?

Accepted Answer

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

Question 3

Find the vertex of the parabola $f(x) = 2(x - 1)^2 + 3$.

Accepted Answer

$(1, 3)$

Question 4

Which of the following is the solution to $\log_2(x - 1) + 2\log_2(x) = 3$?

Accepted Answer

$x = 4$

Question 5

A population grows according to $P(t) = 10,000e^{0.07t}$. How many years will it take for the population to double?

Accepted Answer

$t = \frac{\ln 2}{0.07}$

Question 6

Which of the following is the equation of the line parallel to $y = 2x - 5$ and passing through $(4, 6)$?

Accepted Answer

$y = 2x - 2$

Question 7

Given $f(x) = x^3 - 3$ and $g(x) = x - 2$, find $(f \circ g)(x)$.

Accepted Answer

$(x - 2)^3 - 3$

Question 8

Find the inverse of the function $f(x) = 2x + 1$.

Accepted Answer

$f^{-1}(x) = \frac{x - 1}{2}$

Question 9

Solve the system of equations: $\begin{cases} 2x + y = 4 \ x - y = 1 \end{cases}$.

Accepted Answer

$x = 1.67,\ y = 0.67$

Question 10

Which of the following is the domain of $f(x) = \frac{2x}{x^2 - 9}$?

Accepted Answer

$x 
eq 3,\ x 
eq -3$

Question 11

If $\log_3(x) = 4$, what is the value of $x$?

Accepted Answer

$x = 81$

Question 12

Find the $y$-intercept of the function $f(x) = x^2 - 4x + 5$.

Accepted Answer

$y = 5$

Question 13

Which of the following is the solution to $|2x - 3| < 1$?

Accepted Answer

$1 < x < 2$

Question 14

A bank offers an interest rate of $5\%$ compounded quarterly. What is the effective annual rate?

Accepted Answer

$5.09\%$

Question 15

Which of the following is the sum $\sum_{k=1}^4 (k^2 - 2)$?

Accepted Answer

$24$

Question 16

Given $f(x) = 2x^2 - 3x^2 - 5x + 6$, factor $f(x)$ into linear factors.

Accepted Answer

$-(x - 6)(x - 1)$

Question 17

Which of the following is the simplified form of $\frac{1}{2}\log_a x + 4\log_a y - 3\log_a z$ as a single logarithm?

Accepted Answer

$\log_a \left( \frac{\sqrt{x} y^4}{z^3} \right)$

Question 18

If $f(x) = \frac{2x}{x - 3}$, what is the horizontal asymptote?

Accepted Answer

$y = 0$

Question 19

Suppose two cars start 120 km apart and drive toward each other at 60 km/h and 40 km/h. How long until they meet?

Accepted Answer

$2$ hours

Question 20

Which of the following is the solution to $2x^2 + 3x - 2 = 0$?

Accepted Answer

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

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions