Q: Which of the following matrices is invertible?

$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$

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

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

Q: Which of the following is the solution set for the inequality $x^2 - 4x < 5$?

$2 - \sqrt{9} < x < 2 + \sqrt{9}$

Q: Which of the following statements about the determinant of a matrix is true?

A matrix is invertible if and only if its determinant is not zero.

Question 1

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

Accepted Answer

A relation in which 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 graphs represents a function that is one-to-one?

Accepted Answer

A straight line with a nonzero slope.

Question 4

If $g(x) = \sqrt{x-1}$, what is the domain of $g(x)$?

Accepted Answer

$x \geq 1$

Question 5

Which of the following is the correct inverse of the function $f(x) = 3x + 7$?

Accepted Answer

$f^{-1}(x) = \frac{x-7}{3}$

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 	imes 3^{t/4}$

Question 7

Solve for $x$: $2^{x+1} = 32$

Accepted Answer

$x = 4$

Question 8

Which of the following is a solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 9

Given the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$, what is the value of $x$?

Accepted Answer

$x = 2$

Question 10

Which of the following matrices is invertible?

Accepted Answer

$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$

Question 11

A quadratic function models the height $h$ (in meters) of a ball thrown upward from the ground as $h(t) = -4.9t^2 + 20t$. What is the maximum height reached by the ball?

Accepted Answer

$20.41$ meters

Question 12

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x-4)(x-5)$

Question 13

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

Accepted Answer

$9$

Question 14

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

Accepted Answer

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

Question 15

A chemical reaction is modeled by the exponential decay function $C(t) = 100e^{-0.05t}$, where $C$ is the concentration in mg/L and $t$ is time in minutes. What is the concentration after 20 minutes?

Accepted Answer

$C(20) \approx 60.65$ mg/L

Question 16

Which of the following is the solution set for the inequality $x^2 - 4x < 5$?

Accepted Answer

$2 - \sqrt{9} < x < 2 + \sqrt{9}$

Question 17

Which of the following statements about the determinant of a matrix is true?

Accepted Answer

A matrix is invertible if and only if its determinant is not zero.

Question 18

A medical test result is modeled by the function $T(x) = \frac{1}{1+e^{-x}}$. If $x = 0$, what is the value of $T(x)$?

Accepted Answer

$0.5$

Question 19

Which of the following is the correct solution to the equation $|2x - 5| = 9$?

Accepted Answer

$x = 7$ or $x = -2$

Question 20

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$P = 20$ thousand dollars

College Algebra Syllabus and Course Outline Study Guide

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