Question 1

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

Accepted Answer

$$x 
eq 2,\ x 
eq -2$$

Question 2

A medical dosage formula is given by $$D(t) = \frac{100}{t-3}$$, where $$t is $$the time in hours after administration. What is the vertical asymptote of $$D(t)$$?

Accepted Answer

$$t = 3$$

Question 3

Given the function $$f(x) = 3x + 5$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 4

Which of the following graphs represents an exponential growth function?

Accepted Answer

$$y = 4^x$$

Question 5

A population of bacteria doubles every 3 hours. Which equation models the population $$P$$ after $$t$$ hours, if the initial population is $$P_0$$?

Accepted Answer

$$P = P_0$ \cdot 2$$^{t/3}$$

Question 6

Which property of logarithms allows you to write $$\log_b(xy) as$$ $$\log_b(x) + \log_b(y)$$?

Accepted Answer

Product property

Question 7

Expand the logarithmic expression $$\log_2$(8x)$$ using properties of logarithms.

Accepted Answer

$$\log_2$(8) + \log_2$(x)$$

Question 8

Solve for $$x$$: $$2^x = 16.$$

Accepted Answer

$$x = 4$$

Question 9

A scientist measures the pH of a solution as $$pH = -\log_{10}[H^+]. If$$ $$[H^+] = 1 	imes 10$$^{-5}$$, what is the pH?

Accepted Answer

$$pH = 5$$

Question 10

Which of the following is the correct inverse of the exponential function $$f(x) = e$$^{2x}$$?

Accepted Answer

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

Question 11

Which of the following is equivalent to $$\log_5$(125)$$?

Accepted Answer

$$3$$

Question 12

If $$f(x) = \frac{1}{x-1}$$, which value of $$x$$ makes $$f(x)$$ undefined?

Accepted Answer

$$x = 1$$

Question 13

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 14

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.2t}$$. What is the half-life of the substance?

Accepted Answer

$$t = \frac{\ln(2)}{0.2}$$

Question 15

Which of the following is the correct application of the change of base formula for $$\log_7$(50)$$?

Accepted Answer

$$\frac{\log_{10}(50)}{\log_{10}(7)}$$

Question 16

Which of the following expressions is equivalent to $$\ln(x^2$y)$$?

Accepted Answer

$$2\ln(x) + \ln(y)$$

Question 17

Solve for $$x$$: $$\log_3$(x-2) = 4.$$

Accepted Answer

$$x = 82$$

Question 18

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

Accepted Answer

$$20000 \cdot 0.85^3$

Question 19

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

Accepted Answer

$$x = \ln(7)$$

College Algebra Exam #3 Study Guide: Rational, Inverse, Exponential, and Logarithmic Functions

Guida di studio - Domande di pratica

Study guide - Flashcard