which statement is incorrect for the graph of the function y = - 3 cos 3/π(x - 4)+7? circle the incorrect…

Explanation:

Step1: Recall cosine - function general form

The general form of a cosine function is $y = A\cos(B(x - C))+D$, where $A$ is the amplitude, $B$ affects the period, $C$ is the phase - shift, and $D$ is the vertical shift (mid - line). For the function $y=-3\cos\left[\frac{\pi}{3}(x - 4)\right]+7$, we have $A=-3$, $B = \frac{\pi}{3}$, $C = 4$, and $D = 7$.

Step2: Calculate the amplitude

The amplitude of a cosine function $y = A\cos(B(x - C))+D$ is given by $|A|$. Here, $|A|=|-3| = 3$, so the amplitude is 3.

Step3: Calculate the mid - line

The mid - line of the cosine function $y = A\cos(B(x - C))+D$ is $y = D$. Here, $D = 7$, so the mid - line is $y = 7$, not $y=-4$.

Step4: Calculate the range

The range of $y=\cos t$ is $[-1,1]$. For $y=-3\cos\left[\frac{\pi}{3}(x - 4)\right]+7$, when $\cos\left[\frac{\pi}{3}(x - 4)\right]=-1$, $y=-3\times(-1)+7=3 + 7=10$; when $\cos\left[\frac{\pi}{3}(x - 4)\right]=1$, $y=-3\times1+7=-3 + 7 = 4$. So the range is $[4,10]$.

Answer:

The midline is $y=-4$.