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 end behavior of the polynomial $$f(x) = -2x^4$ + 5x^3$ - x + 7$$?

Accepted Answer

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

Question 2

Given the rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$, which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $$x = 2$$ and $$x = -2$$

Question 3

Which of the following is a possible rational zero of $$f(x) = 2x^3$ - 3x^2$ + x - 6$$ according to the Rational Root Theorem?

Accepted Answer

$$\frac{3}{2}$$

Question 4

If $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use synthetic division to determine the remainder when $$f(x) is $$divided by $$x - 2.$$

Accepted Answer

$$2$$

Question 5

Which of the following best describes the horizontal asymptote of $$f(x) = \frac{3x^2$ + 1}{x^2$ - 4}$$?

Accepted Answer

$$y = 3$$

Question 6

A population of bacteria triples every 2 hours. If the initial population is 100, which exponential function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 3$$^{t/2}$$

Question 7

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

Accepted Answer

$$x = 3$$

Question 8

Which of the following is equivalent to $$\log_2$ 32$$?

Accepted Answer

$$5$$

Question 9

If $$\log_b 8 = 3$$, what is the value of $$b$$?

Accepted Answer

$$2$$

Question 10

Which of the following is the correct application of the change of base formula for $$\log_5$ 20$$?

Accepted Answer

$$\frac{\log_{10} 20}{\log_{10} 5}$$

Question 11

Solve the system: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1.5$$

Question 12

Which of the following sequences is geometric?

Accepted Answer

$$2, 4, 8, 16, 32$$

Question 13

Find the sum of the first 5 terms of the arithmetic sequence where $$a_1 = 3$ and d = 4$.

Accepted Answer

$$35$$

Question 14

Which of the following is the formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 15

A company’s revenue is modeled by $$R(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$$26$$

Question 16

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x + y) = \log_b x + \log_b y$$

Question 17

If $$f(x) = x^4$ - 5x^2$ + 4$$, how many $$x-$$intercepts does the graph of $$f(x)$$ have?

Accepted Answer

4

Question 18

Which of the following best describes the solution set for the system $$\begin{cases} x + 2y = 4 \ 2x + 4y = 8 \end{cases}$$?

Accepted Answer

Infinitely many solutions

Question 19

Given $$f(x) = x^3$ - 2x^2$ - x + 2$$, which value is a zero of $$f(x)$$?

Accepted Answer

$$x = 2$$

Question 20

Find the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$

Accepted Answer

$$6$$

College Algebra: Polynomial, Rational, Exponential, Logarithmic Functions, Systems, and Sequences

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