Question 1

Given $$f(x) = \frac{7}{\sqrt{4 - x^2$}}$$, which of the following is the domain of $$f(x)$$?

Accepted Answer

$$x \in (-2, 2)$$

Question 2

Martin invests $$2000 in $$two accounts: one at $$2\%$$ simple interest and another at $$9\%$$ simple interest. If he earns $$320 in $$interest after one year, how much did he invest in the $$9\%$$ account?

Accepted Answer

$$800$$

Question 3

Given $$f(x) = x^2$ + 1$$ and $$g(x) = x - 5$$, what is $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

$$\frac{x^2$ + 1}{x - 5}$$

Question 4

Which of the following intervals describes where the function in the graph (Example 1, page 2) is increasing?

Accepted Answer

$$(-2, 1)$$ and $$(3, 5)$$

Question 5

Solve for $$x$$: $$|x - 5| \geq 3$$

Accepted Answer

$$x \leq 2 or$$ $$x \geq 8$$

Question 6

Simplify $$(-3 + 5i)^2$.

Accepted Answer

$$-9 + 30i + 25i^2$ = -34 + 30i$$

Question 7

Given $$f(x) = \sqrt{x - 1}$$ and $$g(x) = \sqrt{x + 4} - 1$$, for which $$x is$$ $$f(x) = g(x)$$?

Accepted Answer

$$x = 5$$

Question 8

Which of the following is the solution to $$|3x - 4| + 7 = 12$$?

Accepted Answer

$$x = \frac{9}{3} or$$ $$x = \frac{-5}{3}$$

Question 9

If $$f(x) = \frac{5}{x - 3}$$ and $$g(x) = \frac{1}{x}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x 
eq 0$$

Question 10

Solve $$6x^2 - 16x = -10$.

Accepted Answer

$$x = 2 or$$ $$x = -0.83$$

Question 11

Which of the following is the simplified form of $$\frac{5 - 3i}{3 - 4i}$$?

Accepted Answer

$$\frac{7 + 11i}{25}$$

Question 12

Given the function $$f(x) = 3 - |x|$$, what is its range?

Accepted Answer

$$(-\infty, 3]$$

Question 13

Which of the following is the solution set for $$|1 - 2x| \leq 4$$?

Accepted Answer

$$-1.5 \leq x \leq 2.5$$

Question 14

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

Accepted Answer

$$x \geq 0$$

Question 15

Which of the following is the correct solution to $$\frac{1}{x - 4} = \frac{1}{x + 4} + \frac{32}{x^2$ - 16}$$?

Accepted Answer

$$x = 8$$

Question 16

Given the graph in Example 3 (page 2), which $$x-$$value is a relative maximum?

Accepted Answer

$$x = 1$$

Question 17

Which of the following pairs of lines are perpendicular?

Accepted Answer

$$y = 2x + 1$$ and $$y = -\frac{1}{2}x + 5$$

Question 18

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

Accepted Answer

$$x \geq 1$$

Question 19

Which of the following is the solution to $$5x - 7)(3x + 4) = 0$$?

Accepted Answer

$$x = \frac{7}{5} or$$ $$x = -\frac{4}{3}$$

Precalculus Study Notes: Functions, Graphs, and Algebraic Techniques

Study Guide - Practice Questions

Study Guide - Flashcards