# Algebra help to find the

**Question description**

1. Now consider the parent function *P(x) = x ^{2}*, and
let g(x) = 4(x-1)

^{2}+ 8.

(A) Explain step-by-step,
graphing/labeling **(on graph paper!)**
the parent, each intermediate function, if we do transformations in these two orders:
(You will have to figure out the exact transformations in each case.)

(i)Horizontal shift then vertical stretch then vertical shift; (ii)Horizontal shift then vertical shift then vertical stretch.

(B) (i) Explain how you can cut the
domain of our *g(x)* so that at least
part of it has an inverse function (I.e. passes the horizontal line test).

(ii) Now find
the equation of the INVERSE function of our *g(x).*

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