the first decision is a choice between y = acosb(x - h)+k and y = asinb(x - h)+k. starting at the green…

Answer:

-cosine

Explanation:

Step1: Recall cosine and sine graphs

The cosine function $y = \cos(x)$ starts at a maximum value when $x = 0$, $y=\sin(x)$ starts at the mid - value ($y = 0$) when $x = 0$. The negative cosine function $y=-\cos(x)$ starts at a minimum value.

Step2: Analyze the given pattern

The pattern starts at a minimum (green point), then goes to mid - value, then maximum, then mid - value, then minimum again. The graph of $y =-\cos(x)$ has this pattern starting from $x = 0$. So the pattern is that of $-\cosine$.