Question

. (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?

Answer 1

Answer:

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.

Answer 2

Either variable is autonomous can be verified using functional notation. The predictor variable in this example is x. These two quantities (variables) in the problematic situation are months and a bit of exercise.

• Since the amount of exercise relies on how many days have passed, weeks are the underlying factor or x.
• This implies that exercise is proportional to the number of consecutive days.
• It indicates that f(x) is a couple of weeks and x seems to be the amount of exercise.

Therefore, the answer is "The total number of hours exercised is given by f(x), and the number of weeks is given by x".

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