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

Question 1

Which of the following best describes the end behavior of the polynomial $f(x) = -2x^4 + 5x^3 - x + 7$?

Accepted Answer

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

Question 2

Given the rational function $f(x) = \frac{x^2 - 9}{x^2 - 4}$, which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $x = 2$ and $x = -2$

Question 3

Which of the following is a possible rational zero of $f(x) = 2x^3 - 3x^2 + x - 6$ according to the Rational Root Theorem?

Accepted Answer

$\frac{3}{2}$

Question 4

If $f(x) = x^3 - 4x^2 + 5x - 2$, use synthetic division to determine the remainder when $f(x)$ is divided by $x - 2$.

Accepted Answer

$2$

Question 5

Which of the following best describes the horizontal asymptote of $f(x) = \frac{3x^2 + 1}{x^2 - 4}$?

Accepted Answer

$y = 3$

Question 6

A population of bacteria triples every 2 hours. If the initial population is 100, which exponential function models the population after $t$ hours?

Accepted Answer

$P(t) = 100 \cdot 3^{t/2}$

Question 7

Solve for $x$: $2^{x+1} = 16$.

Accepted Answer

$x = 3$

Question 8

Which of the following is equivalent to $\log_2 32$?

Accepted Answer

$5$

Question 9

If $\log_b 8 = 3$, what is the value of $b$?

Accepted Answer

$2$

Question 10

Which of the following is the correct application of the change of base formula for $\log_5 20$?

Accepted Answer

$\frac{\log_{10} 20}{\log_{10} 5}$

Question 11

Solve the system: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 2, y = 1.5$

Question 12

Which of the following sequences is geometric?

Accepted Answer

$2, 4, 8, 16, 32$

Question 13

Find the sum of the first 5 terms of the arithmetic sequence where $a_1 = 3$ and $d = 4$.

Accepted Answer

$35$

Question 14

Which of the following is the formula for the $n$th term of a geometric sequence with first term $a_1$ and common ratio $r$?

Accepted Answer

$a_n = a_1 r^{n-1}$

Question 15

A company’s revenue is modeled by $R(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$26$

Question 16

Which of the following is NOT a property of logarithms?

Accepted Answer

$\log_b(x + y) = \log_b x + \log_b y$

Question 17

If $f(x) = x^4 - 5x^2 + 4$, how many $x$-intercepts does the graph of $f(x)$ have?

Accepted Answer

4

Question 18

Which of the following best describes the solution set for the system $\begin{cases} x + 2y = 4 \ 2x + 4y = 8 \end{cases}$?

Accepted Answer

Infinitely many solutions

Question 19

Given $f(x) = x^3 - 2x^2 - x + 2$, which value is a zero of $f(x)$?

Accepted Answer

$x = 2$

Question 20

Find the sum of the infinite geometric series $3 + 1.5 + 0.75 + \ldots$

Accepted Answer

$6$

College Algebra: Polynomial, Rational, Exponential, Logarithmic Functions, Systems, and Sequences

Study Guide - Practice Questions