What is r and how do you solve for it?

Given f(x) = 17-x^2what is the average rate of change in f(x) over the interval [1, 5]?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3