Question 1

Solve the equation $$|5x-2| = 7. $$What are the solutions?

Accepted Answer

$$x = \frac{9}{5},\ x = -1$$

Question 2

Given the function $$f(x) = \sqrt{x+3}$$, what is its domain?

Accepted Answer

$$[-3, \infty)$$

Question 3

For the function $$f(x) = \frac{x+5}{x^2$ + x - 42}$$, which of the following intervals represents its domain?

Accepted Answer

$$(-\infty, -7) \cup (-7, 6) \cup (6, \infty)$$

Question 4

Which of the following best describes the transformation needed to graph $$g(x) = |x-4| - 2$$ from the basic absolute value function $$f(x) = |x|$$?

Accepted Answer

Shift 4 units right and 2 units down

Question 5

Given the function $$f(x) = x^3$ - \frac{4}{x}$$, determine if the function is even, odd, or neither.

Accepted Answer

Odd

Question 6

Find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 3x + 2$$, $$h 
eq 0.$$

Accepted Answer

$$3$$

Question 7

Given the function $$f(x) = 3x^2$ - 2x + 1$$, evaluate $$f(-2).$$

Accepted Answer

$$17$$

Question 8

A company sells 9000 units at $$2 each and 6000 units at 3 $$each. Assuming a linear relationship, what is the equation relating price $$x to $$number sold $$y$$?

Accepted Answer

$$y = -3000x + 15000$$

Question 9

Given the graph of $$f(x) as a $$parabola with vertex at $$(4, -2)$$, which equation best represents the function?

Accepted Answer

$$f(x) = -\frac{1}{2}(x-4)^2$ + 1$$

Question 10

Find the inverse of the function $$f(x) = \frac{2x+1}{x}.$$

Accepted Answer

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

Question 11

Given $$f(x) = 1 + 5x$$ and $$g(x) = \sqrt{x-1}$$, what is the domain of $$(f+g)(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 12

Which of the following best describes the symmetry of the function $$f(x) = 5x^2$ + 3|x| + 7$$?

Accepted Answer

Even; symmetric about the y-axis

Question 13

Given the function $$f(x) = \sqrt{x+4} - 1$$, what is its domain?

Accepted Answer

$$[-4, \infty)$$

Question 14

Given the piecewise function $$f(x) = \begin{cases} x & 	ext{if } x \leq -1 \ 4 & 	ext{if } x \u003e -1 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$-2$$

Question 15

Given $$f(x) = 3x+1$$ and $$g(x) = 2x-x^2$, what is the domain of $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

$$(-\infty, 0) \cup (0, 2) \cup (2, \infty)$$

Question 16

For the function $$f(x) = x^4$ + 2$$, $$x \leq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = -\sqrt[4]{x-2}$$

Question 17

Given the function $$f(x) = 1 + \sqrt{\frac{x-2}{5}}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 18

Given the graph of $$f(x) as a $$cubic function with origin symmetry, which of the following statements is true?

Accepted Answer

The function is odd and symmetric about the origin.

Question 19

Given $$f(x) = 2x^2$ - 3x - 4$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$4x - 3 + 2h$$

College Algebra Study Guide: Functions, Graphs, and Equations

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