Question

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

Answer 1

Answer:

$f(x) = cos(x - \frac{\pi }{4} ) -1$

Step-by-step explanation:

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

($\frac{5\pi }{4} , -2$), 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 $\frac{\pi }{4}$ and the shift down by 1, our equation is $f(x) = cos(x - \frac{pi}{4} ) - 1$.