Compare g(x) = (x – 2)^3 + 7 to f(x) = (x - h)^3 + k. Here, h denotes horizontal translation and k denotes vertical translation. Translation to the left by 2 units would be (x + 2)^3 + 7. Translation to the right by 2 units would be (x - 2)^3 + 7. So, no, Tia's description of horiz. translation is incorrect.
However, her adding 7 does denote a positive vertical translation.
For fractions if the denominator is the same you go to the numerator (the top number) to compare. The bigger the numerator is (like 6) the higher it should go on your list.