Question

directions: for 6 - 8, graph the following functions.

1. graph ( y = 3 cos left( \frac { 1 } { 2 } x

ight) - 1 )
amplitude:
midline:
period:
phase shift:

1. graph ( y = - 2 sin 2 left( x + \frac { pi } { 4 }

ight) )
amplitude:
midline:
period:
phase shift:

1. graph ( y = 2 - 3 cos pi ( x ) )

amplitude:

Explanation:

Step1: Midline for \(y = -2\sin2(x+\frac{\pi}{4})\)

For a function of the form \(y = A\sin(B(x - C))+D\), the midline is \(y = D\). Here \(A=-2\), \(B = 2\), \(C=-\frac{\pi}{4}\), \(D = 0\). So the midline is \(y = 0\).

Step2: Period for \(y=-2\sin2(x+\frac{\pi}{4})\)

The formula for the period of \(y = A\sin(B(x - C))+D\) is \(T=\frac{2\pi}{|B|}\). Given \(B = 2\), then \(T=\frac{2\pi}{2}=\pi\).

Answer:

Midline: \(0\), Period: \(\pi\)