precalc homework

Math 121 HW6 Due Tuesday, October 16 Please print this homework set. Construct all graphs on the homework set and then scan the solutions. If you use photos, please use an app like CamScanner to convert them to a pdf.

1. Given the equation y = −4sin 2x( ) . a. List the five “key points” in the first period, that is, the points on the

midline and the highest and lowest points. Express the points in coordinate form.

b. Construct the graph.

c. Amplitude = Period = Midline: Phase shift:

2. Given the equation y =3cos x− π 3

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⎝ ⎜

⎞

⎠ ⎟+2

a. Amplitude = Period =

Midline: Phase shift:

b. Graph y =3cos x− π 3

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⎝ ⎜

⎞

⎠ ⎟+2

3. Given the following graph.

a. Amplitude = Period =

Midline: Phase shift: b. Construct a possible equation for the graph. Use the cosine function.

4. Given the equation y = −2cos 3x+ π 2

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⎝ ⎜

⎞

⎠ ⎟

a. Determine the following:

Amplitude = Period =

Midline: Phase shift:

b. Graph the equation

5. Graph y = −3tanx . Be sure to graph at least two periods.

6. Graph y = −1+2secx . Be sure to graph at least two periods.

7. Given the following graph.

Construct an appropriate equation using the cotangent function for the graph.