Consider the table of values for functions f and g below.

x f(x) g(x)
0 3 3
1 7 11
2 19 19
3 55 27
4 163 35
5 457 43

which of the following statements is true?

a.
for every value of x, the rate of change of f exceeds the rate of change of g.
b.
as x increases, the rate of change of g exceeds the rate of change of f.
c.
as x increases, the rate of change of f exceeds the rate of change of g.
d.
at x = 2, the rate of change of f is equal to the rate of change of g.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?