Question 1

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 2

A population of bacteria doubles every 3 hours. If the initial population is 500, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 3

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 4

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$12.2$$ meters

Question 5

Which of the following is the inverse function of $$f(x) = 3x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 5}{3}$$

Question 6

Which of the following is a solution to the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$x = 3.5$$

Question 7

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream by $$C(t) = 20e$$^{-0.5t}$$, where t$ is in hours. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 20e$$^{-2}$$

Question 8

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

Accepted Answer

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

Question 9

Given the function $$f(x) = \dfrac{x^2$ - 9}{x - 3}$$, for $$x 
eq 3$$, what is $$f(5)$$?

Accepted Answer

$$f(5) = 16$$

Question 10

Which of the following describes the graph of $$y = |x - 2|$$?

Accepted Answer

A V-shaped graph with vertex at $$(2, 0)$$

Question 11

Which of the following is the solution set for the equation $$\sqrt{x + 3} = x - 1$$?

Accepted Answer

$$x = 2$$

Question 12

A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) = 20000 	imes 0.85^3$

Question 13

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

Accepted Answer

$$x = 2, y = 5$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is the correct solution to the quadratic equation $$x^2 + 6x + 5 = 0$?

Accepted Answer

$$x = -1$$ and $$x = -5$$

Question 16

Which of the following is the correct graph for $$y = \log_2$(x)$$?

Accepted Answer

A curve passing through $$(1, 0)$$ and increasing for $$x \u003e 1$$

Question 17

Which of the following is the correct solution to the equation $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5$$ and $$x = -2$$

Question 18

Which of the following is the correct solution to the equation $$\dfrac{x + 2}{x - 1} = 3$$?

Accepted Answer

$$x = 2.5$$

Question 19

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

Accepted Answer

$$x = 4$$

Precalculus Algebra Syllabus and Study Guide

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