Question 1

Which of the following best describes the period of the function $$f(x) = 3 \sin(2x - \frac{\pi}{3}) + 1$$?

Accepted Answer

$$\pi$$

Question 2

Given the function $$f(x) = a^x$$ with $$a \u003e 0$$ and $$a 
eq 1$$, which of the following statements is TRUE?

Accepted Answer

The function is invertible and its inverse is $$f^{-1}(x$$) = \log_a(x)$$.

Question 3

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$32$$

Question 4

Which transformation will reflect the graph of $$y = \sin(x)$$ over the x-axis?

Accepted Answer

$$y = -\sin(x)$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is the correct domain of the function $$f(x) = \log_5$(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 7

If $$f(x) = 2^x$$ and $$g(x) = \log_2$(x)$$, which statement is TRUE?

Accepted Answer

$$f(g(x)) = x$$ for all $$x \u003e 0.$$

Question 8

Which of the following is equivalent to $$\log_3$(27) + \log_3$(1/3)$$?

Accepted Answer

$$0$$

Question 9

A function $$f$$ passes the horizontal line test. What can you conclude?

Accepted Answer

The function is one-to-one and invertible.

Question 10

Which of the following is the correct range of the function $$f(x) = \arcsin(x)$$?

Accepted Answer

$$[-\frac{\pi}{2}, \frac{\pi}{2}]$$

Question 11

Suppose $$f(x) = 4^x$$ and $$g(x) = \log_4$(x). $$What is $$f(g(16))$$?

Accepted Answer

$$16$$

Question 12

Which of the following is a property of all one-to-one functions?

Accepted Answer

They pass the horizontal line test.

Question 13

If $$f(x) = \sin(x)$$, which of the following restrictions on the domain makes $$f$$ one-to-one?

Accepted Answer

$$[-\frac{\pi}{2}, \frac{\pi}{2}]$$

Question 14

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 100$$ grams and $$k = 0.2$$, how much remains after 5 hours? (Round to the nearest gram.)

Accepted Answer

$$37$$ grams

Question 15

Which of the following is NOT a correct logarithmic property?

Accepted Answer

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

Question 16

If $$f(x) = \cos(x)$$, what is the amplitude of $$f(x)$$?

Accepted Answer

$$1$$

Question 17

Which of the following real-world scenarios can be modeled by an exponential function?

Accepted Answer

The height of a bouncing ball after each bounce (assuming a constant ratio).

Question 18

If $$\log_{10}(x) = 2$$, what is $$x$$?

Accepted Answer

$$100$$

Question 19

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

Accepted Answer

It is one-to-one on $$(-\frac{\pi}{2}, \frac{\pi}{2}).$$

Question 20

Which of the following is the correct inverse of $$f(x) = e^x$$?

Accepted Answer

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

Trig, Exponentials, Logs, and Inverses: Foundations for Calculus

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