When a function q(x) is translated up w units, where w > 0, the resulting function, say t(x),
can be described by t(x) = q(x) + w.
Here, when g(x) = x^3 + 1 is translated to the right 4 units, the resulting function, say v(x), can
be described by v(x) = g(x − 4) = (x − 4)^3 + 1. When the function v(x) is translated 2 units up,
the resulting function, which the question stem says is h(x), can be described by h(x) = v(x) + 2
= [(x − 4)^3 + 1] + 2 = (x − 4)^3 + 3.
Thus, h(x) = (x − 4)^3 + 3.
Then h(3.7) = (3.7 − 4)^3 + 3 = (−0.3)^3 + 3 = −0.027 + 3 = 2.973.
We can draw graphs of both g(x) and h(x).
47 . C
The number of five-letter codes possible is the number of ways of permuting 5 different
objects from 12 different objects. Say that nPk is the number of ways to permute k different
objects from n different objects, where n is a positive integer and k is an integer such that 0 ≤
k ≤ n. Then . In this question, n = 12 and k = 5. The number of possible five-
letter codes is .
