8.1E: Graphs of the Sine and Cosine Functions (Exercises)

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.

1. \(f(x)=-3 \cos x+3\)

2. \(f(x)=\frac{1}{4} \sin x\)

3. \(f(x)=3 \cos \left(x+\frac{\pi}{6}\right)\)

4. \(f(x)=-2 \sin \left(x-\frac{2 \pi}{3}\right)\)

5. \(f(x)=3 \sin \left(x-\frac{\pi}{4}\right)-4\)

6. \(f(x)=2\left(\cos \left(x-\frac{4 \pi}{3}\right)+1\right)\)

7. \(f(x)=6 \sin \left(3 x-\frac{\pi}{6}\right)-1\)

8. \(f(x)=-100 \sin (50 x-20)\)

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