question 5 of 10 let the function f(x) have t...
question 5 of 10 let the function f(x) have the form f(x) = acos(x + c). to produce a graph that matches the one shown below, what must the value of a be? click here for long description a. 1 b. 3 c. 4 d. 2
Answer
# Explanation:
## Step1: Recall amplitude - formula
The general form of a cosine function is $y = A\cos(x + C)$, and the amplitude is given by $|A|$. The amplitude is the distance from the mid - line of the graph to the maximum or minimum value of the function.
## Step2: Determine mid - line and max/min
The mid - line of the given cosine graph is $y = 0$. The maximum value of the function on the graph is $y = 4$ and the minimum is $y=-4$.
## Step3: Calculate amplitude
The amplitude $|A|=\frac{\text{max}-\text{min}}{2}$. Substituting $\text{max} = 4$ and $\text{min}=-4$ into the formula, we get $|A|=\frac{4 - (-4)}{2}=\frac{8}{2}=4$. Since the graph is not reflected (the cosine function starts at a minimum or maximum as a normal cosine - like shape), $A = 4$.
# Answer:
C. 4