$$f(x) = \begin{cases} 2x + 4 & x \geq 0 \\ 2x + 4 & x \u003c 0 \end{cases}$$

$$\theta = \pi,\ \theta = \dfrac{2\pi}{3},\ \theta = 0$$

$$x \neq 3,\ x \neq -\dfrac{1}{2}$$

$$\theta = 0,\ \pi,\ \dfrac{\pi}{2}$$

Question 1

Which of the following is the correct domain for the function $$f(x) = \dfrac{1}{x^2$ - 16}$$?

Accepted Answer

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

Question 2

Given $$f(x) = 2x + 4$$, rewrite $$f(x) as a $$piecewise function for $$x \geq 0$$ and $$x \u003c 0.$$

Accepted Answer

$$f(x) = \begin{cases} 2x + 4 & x \geq 0 \ 2x + 4 & x \u003c 0 \end{cases}$$

Question 3

Simplify the expression $$\dfrac{x^2$ + 5x + 6}{x^2$ + 5x + 6}$$ for $$x 
eq -2,\ x 
eq -3.$$

Accepted Answer

$$1$$

Question 4

Given $$\cos 	heta = -\dfrac{2}{3}$$ and $$	heta is in $$quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{\sqrt{5}}{3}$$

Question 5

Which of the following is the correct factorization of $$2x^2 - 5x - 3$?

Accepted Answer

$$(2x + 1)(x - 3)$$

Question 6

If $$\sin(	heta) = -\dfrac{3}{5}$$ and $$	heta is in $$quadrant IV, what is $$\cos(	heta)$$?

Accepted Answer

$$\dfrac{4}{5}$$

Question 7

Simplify $$\cos(	heta - \dfrac{\pi}{2}).$$

Accepted Answer

$$\sin 	heta$$

Question 8

Given $$\sin 45^\circ = \dfrac{\sqrt{2}}{2}$$ and $$\cos 30^\circ = \dfrac{\sqrt{3}}{2}$$, find $$\sin(75^\circ).$$

Accepted Answer

$$\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 9

Solve for $$x$$: $$x^2 - 2x = 8$.

Accepted Answer

$$x = 4,\ x = -2$$

Question 10

Given $$\cos x = \dfrac{3}{5}$$ and $$\sin y = \dfrac{5}{13}$$, both in quadrant I, find $$\cos(x + y).$$

Accepted Answer

$$\dfrac{12}{65}$$

Question 11

Which of the following is the correct simplification for $$\dfrac{x^2$ + 3x - 4}{x^2$ + 5x + 6}$$?

Accepted Answer

$$\dfrac{x - 1}{x + 2}$$

Question 12

Solve for $$	heta in$$ $$2\cos 	heta + \cos^2$ 	heta = 0$$ for $$0 \leq 	heta \u003c 2\pi.$$

Accepted Answer

$$	heta = \pi,\ 	heta = \dfrac{2\pi}{3},\ 	heta = 0$$

Question 13

If $$	an 	heta = -1$$ and $$	heta is in $$quadrant II, what is $$	heta$$?

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 14

Given $$f(x) = x^2$ + 3x - 4$$, factor $$f(x)$$ completely.

Accepted Answer

$$(x + 4)(x - 1)$$

Question 15

Which of the following is the correct domain for $$g(x) = \dfrac{1}{2x^2$ - 5x - 3}$$?

Accepted Answer

$$x 
eq 3,\ x 
eq -\dfrac{1}{2}$$

Question 16

If $$\sin^2$ 	heta + \cos^2$ 	heta = 1$$, what is $$\cos^2$ 	heta in $$terms of $$\sin^2$ 	heta$$?

Accepted Answer

$$1 - \sin^2$ 	heta$$

Question 17

Solve for $$	heta in$$ $$2\sin 	heta \cos 	heta = \sin 	heta$$ for $$0 \leq 	heta \u003c 2\pi.$$

Accepted Answer

$$	heta = 0,\ \pi,\ \dfrac{\pi}{2}$$

Question 18

Given $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 19

If $$f(x) = x^2$ + 4x$$, factor $$f(x)$$ completely.

Accepted Answer

$$x(x + 4)$$

Precalculus Study Notes: Functions, Factoring, Domains, and Trigonometric Equations

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