The function f(x) = x1/3 is transformed to get function h. h(x) = (2x)1/3 + 5
which statements are true about function h?

A. as x approaches infinity, h(x) approaches infinity
B. as x approaches negative infinity, h(x) approaches negative infinity
C. the x-intercept is (5,0)
D. the domain of h is (negative infinity, positive infinity)
E. the range of the function is [5, infinity)
F. the y-intercept is (0,5)

Divide. reduce the answer to lowest terms.5 2/3 ÷ 3 1/9

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?

Without any equipment, you can see stars that are 2{,}800{,}0002,800,0002, comma, 800, comma, 000 light-years away. by looking through a small telescope, you can see stars that are 3{,}112{,}000{,}0003,112,000,0003, comma, 112, comma, 000, comma, 000 light-years away. approximately how many times as far can you see using a small telescope as without any equipment?