F(x) = x
g(x) = x+3
how does the graph of g(x) compare with the graph of f(x)?
a the graph of g(x) is more steep and has been shifted 3 units down from the graph of f(x).
b the graph of g(x) is more steep and has been shifted 3 units up from the graph of f(x).
c the graph of g(x) is less steep and has been shifted 3 units down from the graph of f(x).
d the graph of g(x) is less steep and has been shifted 3 units up from the graph of f(x).

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?