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

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 transformation for $f(x) = (x+2)^2 - 5$ compared to $f(x) = x^2$?

Shift left 2 units and down 5 units

Question 1

Which of the following best describes the domain of the function $f(x) = \sqrt{2x - 5}$?

Question 2

A quadratic function models the height $h$ (in meters) of a ball $t$ seconds after it is thrown: $h(t) = -4.9t^2 + 20t + 1.5$. What is the maximum height the ball reaches?

Accepted Answer

$21.96$ meters

Question 3

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

Accepted Answer

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

Question 4

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). For what value of $x$ is the profit maximized?

Accepted Answer

$x = 4$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is the solution set for the inequality $2x^2 - 5x + 2 < 0$?

Accepted Answer

$1 < x < 2$

Question 7

Given $f(x) = x^2 - 4$ and $g(x) = 2x + 1$, what is $(f \circ g)(x)$?

Accepted Answer

$(2x + 1)^2 - 4$

Question 8

Which of the following is the equation of a circle with center $(2, -3)$ and radius $5$?

Accepted Answer

$(x - 2)^2 + (y + 3)^2 = 25$

Question 9

A population of bacteria triples every 4 hours. If the initial population is 200, what is the population after 12 hours?

Accepted Answer

$200 	imes 3^3 = 5400$

Question 10

Which of the following is the correct factorization of $x^3 - 8$?

Accepted Answer

$(x - 2)(x^2 + 2x + 4)$

Question 11

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

Accepted Answer

$x = 32$

Question 12

If $f(x) = \frac{1}{x-2}$, what is the domain of $f$?

Accepted Answer

$x 
eq 2$

Question 13

Which of the following describes the range of the function $f(x) = |x - 3|$?

Accepted Answer

$y \geq 0$

Question 14

A rational function has a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$. Which of the following could be its equation?

Accepted Answer

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

Question 15

Which of the following is the solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$(2, 1)$

Question 16

Which of the following is the correct solution to the equation $e^{2x} = 7$?

Accepted Answer

$x = \frac{1}{2} \ln 7$

Question 17

Which of the following is the correct graph transformation for $f(x) = (x+2)^2 - 5$ compared to $f(x) = x^2$?

Accepted Answer

Shift left 2 units and down 5 units

Question 18

If $f(x) = 2x^2 - 3x + 1$, what is $f(-2)$?

Accepted Answer

$15$

Question 19

Which of the following is the solution to the equation $|3x - 4| = 5$?

Accepted Answer

$x = 3$, $x = -\frac{1}{3}$

College Algebra (MATH 1600) Syllabus and Course Structure

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