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

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

Q: A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years? (Round to the nearest dollar.)

$20,000 \times (0.85)^3 \approx 12,281$

Question 1

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

Accepted Answer

$x \geq 2.5$

Question 2

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

$P = 200 \cdot 3^{t/4}$

Question 3

Given the quadratic function $f(x) = -2x^2 + 8x - 3$, what are the coordinates of its vertex?

Accepted Answer

$(2, 5)$

Question 4

Which of the following is the inverse of the function $f(x) = 5x - 7$?

Question 5

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = -2x^2 + 12x + 20$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $R(3) = 38$ at $x = 3$ thousand units

Question 6

Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$

Accepted Answer

$x = 2, y = 1$

Question 7

Which of the following intervals describes where the function $f(x) = x^2 - 4x + 3$ is decreasing?

Accepted Answer

$(2, \infty)$

Question 8

If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $(f \circ g)(3)$?

Accepted Answer

$f(g(3)) = 2 \cdot 9 + 1 = 19$

Question 9

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

Accepted Answer

$-1 < x < 6$

Question 10

A radioactive substance decays according to $A(t) = 100e^{-0.05t}$, where $A$ is the amount remaining after $t$ years. How much remains after 20 years (rounded to the nearest whole number)?

Accepted Answer

$A(20) = 100e^{-1} \approx 37$

Question 11

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

Accepted Answer

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

Question 12

Given $f(x) = \log_2(x - 1)$, what is the domain of $f$?

Accepted Answer

$x > 1$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$x = 3$

Question 15

Which of the following is the solution to the equation $\log_3(x) = 4$?

Accepted Answer

$x = 81$

Question 16

A quadratic equation $ax^2 + bx + c = 0$ has no real solutions if:

Accepted Answer

$b^2 - 4ac < 0$

Question 17

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

Accepted Answer

$f(2) + g(2) = 4 + 3 = 7$

Question 18

Which of the following best describes the range of the function $f(x) = e^x$?

Accepted Answer

$(0, \infty)$

Question 19

A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years? (Round to the nearest dollar.)

Accepted Answer

$20,000 	imes (0.85)^3 \approx 12,281$

College Algebra Syllabus and Study Guide

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