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

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

Question 1

Which of the following best describes the main purpose of using multiple representations (algebraic, graphic, numeric, and verbal) of functions in precalculus algebra?

Accepted Answer

To describe relationships between quantities from different perspectives and enhance understanding.

Question 2

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

Accepted Answer

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

Question 3

Given the function $$f(x) = x^2$ - 4x + 3$$, which of the following is the correct factorization?

Accepted Answer

$$f(x) = (x - 3)(x - 1)$$

Question 4

Which of the following statements is TRUE about the function $$f(x) = x^3$?

Accepted Answer

It is an odd function.

Question 5

A radioactive substance has a half-life of 10 years. If the initial mass is 80 grams, what is the mass $$M$$ remaining after 30 years?

Accepted Answer

$$M = 80 \cdot \left(\frac{1}{2}\$$right)^{3}$$

Question 6

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 7

A business's profit $$P (in $$dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18$$ dollars at $$x = 2$$ units. (Vertex: $$x = -\frac{b}{2a} = -\frac{8}{2 	imes -2} = 2$$; $$P(2) = -2(2)^2$ + 8(2) + 10 = -8 + 16 + 10 = 18)$$

Question 8

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

Accepted Answer

$$x = 4$$

Question 9

Given the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 10

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

Accepted Answer

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

Question 11

Which of the following is the correct simplification of $$\sqrt[3]{x^6$}$$ for $$x \geq 0$$?

Accepted Answer

Question 12

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 13

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

Accepted Answer

$$2x^2 + 1$

Question 14

Which of the following is the correct solution to the inequality $$|2x - 3| \u003c 5$$?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 15

Which of the following is the correct application of the properties of logarithms to simplify $$\log_{2}(8x)$$?

Accepted Answer

$$\log$$_{2}$$8 + \log$$_{2}$$x$$

Question 16

A company’s revenue $$R is $$given by $$R(x) = 50x - 0.5x^2$, where x$ is the number of units sold. For what value of x$ is the revenue maximized?

Accepted Answer

$$x = 50$$

Question 17

Which of the following is the correct solution to the equation $$\log_{3}(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 18

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

Accepted Answer

Shift right 3 units and up 2 units.

Question 19

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

Accepted Answer

$$x = 1 or$$ $$x = 5$$

MTH 160: Precalculus Algebra Syllabus and Course Overview

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