The absolute value parent function, f(x) = |x| , is transformed to g(x) = |x+3| - 1 and h(x) = |x-2| + 4. Analyze the graphs of g(x) and h(x), independently, to determine the effects of the changes of each from the parent function; lastly, compare g(x) and h(x). Which of the following statements below are true?
I. The function g(x) is translated right 3 units and down 1 unit from f(x).
II. The function h(x) is translated right 2 units and up 4 units from f(x)
III. The x-intercept of g(x) is (-2, 0)
IV. The function h(x) is translated right 5 units and up 5 units from g(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?