Question 1

Given the function $$f(x) = \frac{x-1}{x^2$-16}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 4$$ and $$x = -4$$

Question 2

Find the domain of $$f(x) = \sqrt{1-2x}.$$

Accepted Answer

$$x \leq \frac{1}{2}$$

Question 3

Which of the following is the correct difference quotient for a function $$f(x)$$?

Accepted Answer

$$\frac{f(x+h)-f(x)}{h}$$

Question 4

Given $$f(x) = \frac{2x+2}{x^2$-7x+10}$$, which values must be excluded from the domain?

Accepted Answer

$$x = 2$$ and $$x = 5$$

Question 5

Which of the following is the correct way to convert $$\log_t e = c to $$exponential form?

Accepted Answer

$$t^c = e$$

Question 6

Solve for $$x$$: $$16^x = 7$$

Accepted Answer

$$x = \frac{\ln 7}{\ln 16}$$

Question 7

If $$f(x) = \frac{-6}{x}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 0$$

Question 8

Which of the following is the correct exponential equation for $$5^x = 625$$?

Accepted Answer

$$x = 4$$

Question 9

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

Accepted Answer

$$x \leq 1$$

Question 10

Which of the following is the correct logarithmic form for $$\ln N = e$$?

Accepted Answer

$$N = e^e$$

Question 11

Which of the following is the correct exponential form for $$4^x = 32$$?

Accepted Answer

$$x = \frac{5}{2}$$

Question 12

Which of the following is the correct logarithmic form for $$\log \pi = c$$?

Accepted Answer

$$10^c = \pi$$

Question 13

If $$f(x) = 3 - x^2$, what is the range of f(x$$)$$?

Accepted Answer

$$(-\infty, 3]$$

Question 14

Which of the following is the correct way to write the difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{(x+h)^2$ - x^2$}{h}$$

Question 15

Which of the following is the correct exponential form for $$\log_t e = c$$?

Accepted Answer

$$t^c = e$$

Question 16

If $$f(x) = \frac{x-1}{x^2$-16}$$, which values must be excluded from the domain?

Accepted Answer

$$x = 4$$ and $$x = -4$$

Question 17

Which of the following is the correct logarithmic form for $$5^x = 625$$?

Accepted Answer

$$x = \log_5$ 625$$

Question 18

If $$f(x) = \sqrt{1-2x}$$, what is the largest value of $$x in $$the domain?

Accepted Answer

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

Question 19

Which of the following is the correct way to solve $$16^x = 7$$ for $$x$$?

Accepted Answer

$$x = \frac{\ln 7}{\ln 16}$$

Precalculus Study Notes: Functions, Domains, Exponential and Logarithmic Equations

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