Question

How do you graph `y=-2+cos(1/2(x-pi))`?

Answer 1

Graph the cos(x) graph with a few transformations, streches, and shrinks.

Explanation:

This is essentially the cosine graph with a few changes. First, because the expression with x is (x-pi) we must first shift the graph over to the right by pi units.

Next, because that expression is multiplied by half, we will double the length of the period. This is because it takes twice the magnitude of x to get the same output of y.

Next because two is subtracted from that entire cosine expression we will shift every y value down by two. So the graph just shifts down two units. Hope I helped!