Question 1

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

Accepted Answer

$$x 
eq 4,\ x 
eq -4$$

Question 2

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

Accepted Answer

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

Question 3

What is the difference quotient for $$f(x)$$?

Accepted Answer

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

Question 4

Which of the following is the correct domain for $$f(x) = \frac{2x+2}{x^2$-7x+10}$$?

Accepted Answer

$$x 
eq 2,\ x 
eq 5$$

Question 5

If $$f(x) = -3x^2$, which of the following describes the graph of f(x$$)$$?

Accepted Answer

A parabola opening downward

Question 6

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

Accepted Answer

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

Question 7

Which of the following is equivalent to $$\log_t e = c$$?

Accepted Answer

$$t^c = e$$

Question 8

What is the value of $$x$$ that satisfies $$5^x = 625$$?

Accepted Answer

$$x = 4$$

Question 9

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

Accepted Answer

$$N = e^e$$

Question 10

Find the domain of $$f(x) = \frac{-6}{x}.$$

Accepted Answer

$$x 
eq 0$$

Question 11

If $$4^x = 32$$, what is the value of $$x$$?

Accepted Answer

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

Question 12

Which of the following is the correct domain for $$f(x) = \sqrt{1-x}$$?

Accepted Answer

$$x \leq 1$$

Question 13

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

Accepted Answer

$$t^c = e$$

Question 14

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 15

Which of the following is the correct logarithmic form for $$t^c = e$$?

Accepted Answer

$$\log_t e = c$$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

$$(0,0)$$

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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