Q: A medication decays in the bloodstream according to $A(t) = 50(0.8)^t$, where $A$ is the amount in mg and $t$ is time in hours. How much remains after 3 hours?

$A(3) = 50 \times (0.8)^3 = 25.6$ mg

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?

$20,000 \times (0.85)^3 = 12,282.5$

Q: Which of the following is the range of the function $f(x) = \dfrac{1}{x}$?

$(-\infty, 0) \cup (0, \infty)$

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

As $x \to \pm\infty$, $f(x) \to -\infty$

Question 1

Which of the following best describes the domain of the function $f(x) = \sqrt{2x - 8}$?

Accepted Answer

$x \geq 4$

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

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

Question 3

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

Accepted Answer

$x = 4$

Question 4

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

Accepted Answer

$f^{-1}(x) = \dfrac{x+7}{5}$

Question 5

A chemical reaction follows the equation $C = 10e^{-0.2t}$, where $C$ is the concentration in mg/L and $t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$C = 10e^{-1} \approx 3.68$ mg/L

Question 6

Which of the following is the correct factorization of the quadratic $x^2 - 5x + 6$?

Accepted Answer

$(x-2)(x-3)$

Question 7

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

Accepted Answer

$9$

Question 8

A medication decays in the bloodstream according to $A(t) = 50(0.8)^t$, where $A$ is the amount in mg and $t$ is time in hours. How much remains after 3 hours?

Accepted Answer

$A(3) = 50 	imes (0.8)^3 = 25.6$ mg

Question 9

Which of the following describes the transformation of the graph of $y = x^2$ to $y = (x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 10

Solve the equation $\log_2(x) = 5$ for $x$.

Accepted Answer

$x = 32$

Question 11

A rational function is given by $f(x) = \dfrac{2x+1}{x-4}$. What is the vertical asymptote?

Accepted Answer

$x = 4$

Question 12

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

Accepted Answer

$17$

Question 13

Which of the following is equivalent to $\log_{10}(1000)$?

Accepted Answer

$3$

Question 14

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the area?

Accepted Answer

$216$ square units

Question 15

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

Accepted Answer

$x < 6$

Question 16

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

Accepted Answer

$64$

Question 17

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?

Accepted Answer

$20,000 	imes (0.85)^3 = 12,282.5$

Question 18

Which of the following is the range of the function $f(x) = \dfrac{1}{x}$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 19

Solve for $x$: $x^2 - 9x + 14 = 0$

Accepted Answer

$x = 7$ or $x = 2$

Question 20

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

Accepted Answer

As $x 	o \pm\infty$, $f(x) 	o -\infty$

College Algebra Syllabus and Course Structure Study Guide

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