Practices for Math 140

1. Define a function , whose graph is similar to the cosine function, and satisfies ALL the following conditions:

1. the period of is

2. the function has amplitude of

3. the function has a maximum value of when [hint: You need to come up with ONE function that satisfies All the conditions (a), (b), and (c); think of changing the period, amplitude, reflection, and shifting of

[hint: y=-4cos((1/2)*x)-2].

2. Explain why graphically.  [because if you shift y=sin(x) to the left pi/2 units, you will get y=cos(x)]

3. Express in terms of

4. If

1. Find the period of [**the period is 2*pi divides by (1/3) so it is 6*pi].

2. Find the asymptotes for [**a typo here, it is supposed to be amplitude, the amplitude is 2].

3. Sketch

4. Explain the relationship between the graphs of and [hint: is being reflected along x-axis from and change the amplitude from 1 to 2 and the period of is 6*pi.

5. Find the function whose graph is the reflection of along the [hint: y=cos(-x)]

6. Find the function whose graph is the reflection of along the [hint: y=-sin(-x)].

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