let the function f(x) have the form f(x) = acos(x + c). to produce a graph that matches the one shown below…

Answer:

C. 3

Explanation:

Step1: Recall cosine - function properties

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

Step2: Identify the phase - shift

For the function $y=A\cos(x + C)$, we want to find the value of $C$ such that the graph is shifted to match the given graph. The cosine function $y = \cos x$ has a maximum at $x = 0$. Looking at the given graph of $y=A\cos(x + C)$, the maximum occurs at $x=- 3$. We know that for the function $y = A\cos(x + C)$, when $x + C=0$ (the location of the maximum of the basic cosine - like function), substituting $x=-3$ into $x + C = 0$ gives $-3 + C=0$.

Step3: Solve for $C$

Solving the equation $-3 + C=0$ for $C$ by adding 3 to both sides of the equation, we get $C = 3$.