7. compare the number of relative extrema of the two functions. f(x) has ____ relative extrema, and g(x) has…

Explanation:

Step1: Recall definition of relative extrema

Relative extrema are local maxima and minima. A local maximum is a point where the function changes from increasing to decreasing, and a local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze (f(x))

Looking at the graph of (f(x)), we can see that it has 1 local maximum and 1 local minimum. So in total, (f(x)) has 2 relative extrema.

Step3: Analyze (g(x))

For the graph of (g(x)), it has 2 local maxima and 1 local minimum. So (g(x)) has 3 relative extrema.

Answer:

(f(x)) has 2 relative extrema, and (g(x)) has 3 relative extrema.