Question

2. Find the cosine function that is represented in the graph.

Answer 1

`f(x) = cos(x - (\pi )/(4) ) -1`

Explanation:

In this graph, we have the coordinate point (
`(\pi )/(4) , 0`). Without translations, cos(0) = 0, which means that the graph is shifted to the right by
`(\pi )/(4)`. We also know that the graph is shifted down by 1 because we have the point

(
`(5\pi )/(4) , -2`), but accounting for the right shift, this point should really by (
`\pi , -2`). cos(
`\pi`) = -1, but on the graph it is -2, meaning that it is shifted down by 1.

Therefore, accounting for the right shift by
`(\pi )/(4)` and the shift down by 1, our equation is
`f(x) = cos(x - (pi)/(4) ) - 1`.