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

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

Q: Which of the following is the correct graph for the rational function $f(x) = \frac{2x}{x-1}$?

Vertical asymptote at $x = 1$, horizontal asymptote at $y = 0$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $f(x) = 2x^2 - 3x + 5$, what is $f(-2)$?

Accepted Answer

$f(-2) = 17$

Question 3

Which of the following equations represents a line with a slope of $-4$ and a $y$-intercept of $3$?

Accepted Answer

$y = -4x + 3$

Question 4

Solve the quadratic equation $x^2 - 5x + 6 = 0$.

Accepted Answer

$x = 2$ or $x = 3$

Question 5

What is the domain of the function $f(x) = \frac{1}{x-4}$?

Accepted Answer

$x 
eq 4$

Question 6

Which of the following is the inverse of the function $f(x) = 3x + 2$?

Accepted Answer

$f^{-1}(x) = \frac{x-2}{3}$

Question 7

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 \cdot 2^{t/3}$

Question 8

Solve the system of equations: $\begin{cases} x + y + z = 6 \ 2x - y + 3z = 14 \ -x + 4y - z = -2 \end{cases}$

Accepted Answer

$x = 2, y = 1, z = 3$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$\log_5 20 = \frac{\log_{10} 20}{\log_{10} 5}$

Question 11

A company’s profit $P$ (in dollars) from selling $x$ units is modeled by $P(x) = -2x^2 + 400x - 5000$. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $35,000$ at $x = 100$ units.

Question 12

Which transformation is applied to the graph of $y = x^2$ to obtain $y = (x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units.

Question 13

Which of the following is the correct solution to the inequality $|2x - 5| < 7$?

Accepted Answer

$-1 < x < 6$

Question 14

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(2)$?

Accepted Answer

$(f \circ g)(2) = 9$

Question 15

Which of the following is the correct graph for the rational function $f(x) = \frac{2x}{x-1}$?

Accepted Answer

Vertical asymptote at $x = 1$, horizontal asymptote at $y = 0$

Question 16

Which of the following is equivalent to $\sqrt[3]{x^6}$?

Question 17

Which of the following is the correct solution to the exponential equation $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 18

A radioactive substance decays according to $A(t) = 100e^{-0.05t}$, where $A$ is the amount remaining after $t$ years. How much remains after 10 years?

Accepted Answer

$A(10) = 60.65$

MAC 1105 College Algebra – Course Syllabus and Core Topics Study Guide

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