Study Guide: Topics 3.8-3.10

1

√2

1/√2

2

1

-1

0

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$$\frac{1}{\sqrt[]{3}}$$

$$-\frac{1}{\sqrt[]{3}}$$

$$\sqrt[]{3}$$

$$-\sqrt[]{3}$$

-1/√3

1/√3

√3

-√3

π/3

π/2

π

2π

(A) The period of $$g$$ is $$\pi/3$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{6}+\frac{\pi}{3}k$$ , where $$k$$ is an integer.

(B) The period of $$g$$ is $$\pi/3$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{3}+\pi k$$ , where $$k$$ is an integer.

(C) The period of $$g$$ is $$3\pi$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{3\pi}{2}+3\pi k$$ , where $$k$$ is an integer.

(D) The period of $$g$$ is $$3\pi$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{2}+3\pi k$$ , where $$k$$ is an integer.

For 0 < x < 2π, the graph of g is increasing at an increasing rate.

For 0 < x < 2π, the graph of g is increasing at a decreasing rate.

For 0 < x < 2π, the graph of g is decreasing at an increasing rate.

For 0 < x < 2π, the graph of g is decreasing at a decreasing rate.

A) a > 0 and b > 1

B) a > 0 and b < 1

C) a < 0 and b > 1

D) a < 0 and b < 1

b = π/4 and d = 0

b = π/4 and d = 1

b = 4π and d = 0

b = 4π and d = 1

[-π/2, π/2]

[0, π]

[-π, π]

[π/2, π]