the function (f(x)=acos bx + c) is plotted on the graph shown below.\nwhat are the values of (a), (b), and…

Explanation:

Step1: Find the vertical shift (c)

The mid - line of the cosine function is given by $y = c$. The maximum value of the function is $y = 5$ and the minimum is $y = 1$. The mid - line $c=\frac{5 + 1}{2}=3$.

Step2: Find the amplitude (a)

The amplitude $a$ of a cosine function $y=a\cos(bx)+c$ is given by $a=\frac{\text{Max}-\text{Min}}{2}$. Here, $\text{Max}=5$, $\text{Min}=1$, so $a=\frac{5 - 1}{2}=2$.

Step3: Find the value of b

The period $T$ of the cosine function is the distance between two consecutive maxima or minima. From the graph, the period $T=\frac{\pi}{3}-\frac{\pi}{6}=\frac{\pi}{6}$. The formula for the period of $y = a\cos(bx)+c$ is $T=\frac{2\pi}{|b|}$. Since $T=\frac{\pi}{3}$, we have $\frac{2\pi}{b}=\frac{\pi}{3}$, solving for $b$ gives $b = 6$.

Answer:

A. $a = 2, b = 6, c = 3$