
In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions:
a.
b.
c.
d.
e.
f.
g.
63.

To graph: The each of the following functions:
a.
For the graph function ,
Explanation of Solution
Given:
a.
To obtain the graph of add 3 from each on the graph of , that it is shifted up 3 units.

To graph: The each of the following functions:
b.
For the graph function ,
Explanation of Solution
Given:
b.
To obtain the graph of , replace by on the graph of , that it is shifted left 2 units.

To graph: The each of the following functions:
c.
For the graph function ,
Explanation of Solution
Given:
c.
To obtain the graph of , multiply by on the graph of , that it is reflection about the .

To graph: The each of the following functions:
d.
For the graph function ,
Explanation of Solution
Given:
d.
Now use the following steps to obtain the graph of .
Step 1: To obtain the graph of , replace by from each on the graph of , that it is shifted left 1 unit.
Step 2: To obtain the graph of , subtract 2 from each on the graph of , that it is shifted down 2 units.

To graph: The each of the following functions:
e.
For the graph function ,
Explanation of Solution
Given:
e.
To obtain the graph of , multiply each of the graph of by that it is vertically stretched by the factor of .

To graph: The each of the following functions:
f.
For the graph function ,
Explanation of Solution
Given:
f.
To obtain the graph of , replace by of the graph of , that it is reflection about the .

To graph: The each of the following functions:
g.
For the graph function ,
Explanation of Solution
Given:
g.
To obtain the graph of , replace by of the graph of ; that it is horizontally stretched by the factor of .
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