# How do you graph this function?

Relevance
• ?
Lv 7
1 month ago

The original function y = 2 cos (x/2) goes above and below the x-axis (see dotted-black graph below).

y = | 2 cos (x/2)| simply takes any portion of y = 2 cos (x/2) that falls below the x-axis, and flips it above the x-axis (see solid-lavender graph)

• Pope
Lv 7
1 month ago

Can you graph y = cos(x)? You should be able to do a fair job of that by hand.

Starting with that graph, dilate it with respect to the origin, using scale factor 2. This is a dilation, so it scales the graph in all directions. Actually, you can effect this simply by doubling the indices on both axes, so (..., 1, 2. 3,...) becomes (..., 2, 4, 6,...).

Now for the absolute value part, every part of the graph lying below the x-axis is reflected on that axis so that its image lies above.

• Anonymous
1 month ago

Plug it into desmos my man

• 1 month ago

Cosine curve (U-shaped) with period of 4pi and amplitude of 2. Meaning you start at (0,2) then go down to (2pi,-2) and end at (4pi,2).