select the correct answer. which equation matches the function shown in the graph? a. $y =…

Explanation:

Step1: Recall cosine - function transformation rules

The general form of a cosine function is $y = A\cos(B(x - C))+D$. Here $A = 1$, $B = 1$, $D = 0$. The phase - shift of the cosine function $y=\cos(x)$ is given by $C$. The standard cosine function $y = \cos(x)$ has a maximum at $x = 0$.

Step2: Analyze the phase - shift of the given graph

The standard cosine function $y=\cos(x)$ has a maximum at $x = 0$. The graph of the given function has a maximum at $x=\frac{\pi}{4}$. For the cosine function $y=\cos(x - C)$, when $x - C=0$ (i.e., at the maximum point), if the maximum occurs at $x=\frac{\pi}{4}$, then $C=\frac{\pi}{4}$. So the function is $y=\cos(x-\frac{\pi}{4})$.

Answer:

B. $y = \cos(x-\frac{\pi}{4})$