Question 1

Which of the following is the correct equation for the vertical asymptote of the function $$f(x) = \frac{3x-2}{x^2$-4}$$?

Accepted Answer

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

Question 2

Given the function $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 3

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

Accepted Answer

$$y = 0$$

Question 4

Suppose the population of a bacteria culture triples every 10 hours. Which equation models the population $$P$$ after $$t$$ hours, if the initial population is $$P_0$$?

Accepted Answer

$$P = P_0$ \cdot 3$$^{t/10}$$

Question 5

Which of the following is the correct inverse of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 6

Evaluate $$\log_2$ 32$$ without a calculator.

Accepted Answer

$$5$$

Question 7

Which of the following functions is one-to-one?

Accepted Answer

$$f(x) = x^3$

Question 8

Rewrite $$\ln\left(\frac{x^2$}{y}\right) as a $$sum or difference of logarithms.

Accepted Answer

$$2\ln x - \ln y$$

Question 9

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

Accepted Answer

$$x = 3$$

Question 10

Which of the following is the correct expression for $$\log_3$ 81$$?

Accepted Answer

$$4$$

Question 11

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

Accepted Answer

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

Question 12

Which of the following is the correct expanded form of $$\log_2$(xy^3$$)$?

Accepted Answer

$$\log_2$ x + 3\log_2$ y$$

Question 13

Given $$f(x) = x^2$ - 4$$, which of the following is the $$x-$$intercept?

Accepted Answer

$$(2, 0)$$ and $$(-2, 0)$$

Question 14

Which of the following is the correct solution to $$\log_5$ x = 3$$?

Accepted Answer

$$x = 125$$

Question 15

If $$f(x) = \frac{3x-2}{x^2$-4}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, \frac{1}{2})$$

Question 16

Which of the following is the correct solution for $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 17

Which of the following is the correct expanded form of $$\ln\left(\frac{xy^2$}{z^3$}\right)$$?

Accepted Answer

$$\ln x + 2\ln y - 3\ln z$$

Question 18

If $$f(x) = x^2$, which of the following statements is true?

Accepted Answer

The function is not one-to-one.

Question 19

Which of the following is the correct solution for $$\log_2$(x-1) = 3$$?

Accepted Answer

$$x = 9$$

Question 20

Which of the following is the correct solution for $$\ln(x^2$-1) = 0$$?

Accepted Answer

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

College Algebra: Practice Problems on Functions, Asymptotes, and Logarithms

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