Question

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

In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.

Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.

It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.

Answer 2

f(x) is the total number of hours overall that he has worked out.

x would be the number of weeks he works out.

You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).