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

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

Question 1

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

Accepted Answer

$$x \geq 4$$

Question 2

A biologist models the population of a bacteria culture with the function $$P(t) = 500 \cdot 2$$^{0.3t}$$, where t$ is measured in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500 \cdot 2$$^{1.5}$$ \approx 1414$$

Question 3

Which of the following equations represents a circle in the $$xy-$$plane?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 16$$

Question 4

Given $$f(x) = 3x - 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = 3 \cdot (2^2$) - 5 = 7$$

Question 5

Which of the following is the inverse of the function $$f(x) = \dfrac{x + 4}{3}$$?

Accepted Answer

$$f^{-1}(x) = 3x - 4$

Question 6

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.6$$ meters

Question 7

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

Accepted Answer

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

Question 8

Solve for $$x$$: $$2^{x} = 32$.

Accepted Answer

$$x = 5$$

Question 9

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

Accepted Answer

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

Question 10

A rational function is given by $$f(x) = \dfrac{x^2$ - 9}{x^2$ - 4}. $$What are the vertical asymptotes?

Accepted Answer

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

Question 11

Which of the following is equivalent to $$\log_2$ 8$$?

Accepted Answer

$$3$$

Question 12

Expand the logarithmic expression $$\log_{5}(2x^3$)$$ using properties of logarithms.

Accepted Answer

$$\log$$_{5}$$2 + 3\log$$_{5}$$x$$

Question 13

If $$f(x) = x^2$ + 1$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 14

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 50x - 0.5x^2$, where x$ is the number of units sold (in thousands). What number of units maximizes revenue?

Accepted Answer

$$x = 50$$

Question 15

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

Accepted Answer

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

Question 16

Given the function $$f(x) = \dfrac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $$x = 2$$

Question 17

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

Accepted Answer

$$x = 81$$

Question 18

A quadratic equation $$x^2 + bx + 12 = 0$ has roots x = -3$ and x = -4$. What is the value of b$?

Accepted Answer

$$7$$

Question 19

Which of the following is the result of performing synthetic division of $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$?

Accepted Answer

$$2x^2 + x + 6$ remainder 7$

Question 20

Which of the following is the correct condensed form of $$2\log$$_{7}$$x + \dfrac{1}{2}\log$$_{7}$$y$$?

Accepted Answer

$$\log_{7}\left(\dfrac{x^2$ \sqrt{y}}{1}\right)$$

College Algebra Syllabus and Core Concepts Overview

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