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. $y+1=\cos x$ $y=\cos (x+\pi)$ $y-2=\cos x$ $y=\cos (x-\pi / 2)$ ![](https://cdn.mathpix.com/cropped/2024_09_02_1cfe1a866569e75aed1fg.jpg?height=332&width=1038&top_left_y=410&top_left_x=4)

Solution

Solution Steps

Step 1: Identify the transformation

The black graph is $ y = \cos x $. 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: \[ y = \cos x + 2 \]