Hello, usagi_killer!

I "eyeballed" the two functions . . .

List the sequence of transformations that is necessary to obtain the graph of from

How to do this question algebraically using and method?

Start with: .

Replace with

Add 1: .

. . Hence: .

First, graph

The sequence of transformations is:

(1) Replace with .

. . .This reflects the graph of over the -axis.

(2) Replace with

. . .This contracts the graph to "half its width."

(3) Add 1.

. . .This raises the graph one unit.

The result is the graph of