complete the following statements for the cosine function shown in the graph. the minimum value is -0.75…

Explanation:

Step1: Recall cosine - function form

The general form of a cosine function is $y = A\cos(Bx - C)+D$. The amplitude is $|A|$, the period is $T=\frac{2\pi}{|B|}$, the phase - shift is $\frac{C}{B}$, and the vertical shift is $D$.

Step2: Analyze given values

We know the amplitude $A = 0.75$. The standard cosine function $y=\cos(x)$ has a maximum of 1 and a minimum of - 1. Our function has a maximum of 0.75 and a minimum of - 0.75. There is no phase - shift or vertical shift indicated in the graph.

Step3: Determine the function

Since the amplitude is 0.75 and there are no other transformations (no phase - shift or vertical shift), the equation of the cosine function is $y = 0.75\cos(x)$.

Answer:

$y = 0.75\cos(x)$