(04.07) luke is keeping track of the total number of hours he exercises. he started the summer having already put in 15 hours, and he then exercises 7 hours each week. the function to keep track of his exercise is f(x) = 7x + 15. what do the f(x) and x represent in luke's situation?

f(x) is the total number of hours exercised and x is the number of weeks.

Explanation:

In function notation, we can see which variable is independent.  In this case, x is the independent variable.

In the problem situation, the two quantities (variables) are weeks and amount of exercise; the amount of exercise would depend on how many weeks have passed, so weeks is the independent variable, or x.

This means that exercise is a function of weeks.  This means that f(x) is the amount of exercise, and x is the number of weeks.

Iassume that f' is defined for all real numbers and it's not just defined for the interval shown in the graph.a relative maximum occurs at critical points where f' changes from positive to negative.we are given the graph of f' which is a sinusoidal function with a period of 2. this means if we add the period to a number to be evaluated, we'll get the same thing.we see at x = 1, the graph of f' changes from positive to negative.therefore, the x-values of the relative maxima are    x = 1 + 2n, where n is an integerwe add on 2n as the period is 2.