Practices for Math 140
Define a function , whose graph is similar to the cosine function, and satisfies ALL the following conditions:
the period of is
the function has amplitude of
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].
Explain why graphically. [because if you shift y=sin(x) to the left pi/2 units, you will get y=cos(x)]
Express in terms of
If
Find the period of [**the period is 2*pi divides by (1/3) so it is 6*pi].
Find the asymptotes for [**a typo here, it is supposed to be amplitude, the amplitude is 2].
Sketch
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.
Find the function whose graph is the reflection of along the [hint: y=cos(-x)]
Find the function whose graph is the reflection of along the [hint: y=-sin(-x)].