Questions: Unit Review - Periodic Functions
The black graph is y=cos x.
Skip
Choose the equation for the red graph.
y+1=cos x
y=cos (x+π)
y-2=cos x
y=cos (x-π / 2)
Transcript text: Unit Review - Periodic Functions
The black graph is $y=\cos x$.
Skip
Choose the equation for the red graph.
$y+1=\cos x$
$y=\cos (x+\pi)$
$y-2=\cos x$
$y=\cos (x-\pi / 2)$

Solution
Solution Steps
Step 1: Identify the transformation
The black graph is y=cosx. The red graph appears to be a vertical shift of the black graph. The black graph has a maximum value of 1 at x=0, while the red graph has a maximum value of 3 at x=0.
Step 2: Determine the vertical shift
To find the vertical shift, compare the maximum values of the two graphs. The red graph's maximum value is 3, and the black graph's maximum value is 1. Therefore, the vertical shift is 3−1=2.
Step 3: Write the equation for the red graph
Since the red graph is a vertical shift of the black graph by 2 units upwards, the equation for the red graph is:
y=cosx+2