131
L14
Graphing Techniques: Transformations;
Mathematical Models
Transformations
Vertical and Horizontal Translations: (
0)
c
>
To graph:
shift
( )
f x
c units:
( )
f x
c
+
( )
f x
c
−
(
)
f x
c
+
(
)
f x
c
−
Example:
Graph the function
3
1
y
x
=
−
−
.
132
Vertical Compressions and Stretches:
Example:
Above is the graph of
1
3
y
x
=
. In the same
plane, graph
1
3
2
y
x
=
and
1
3
1
2
y
x
=
.
The graph of
( )
y
a f x
=
(
0
a
≠
) is obtained from
the graph of
( )
y
f x
=
by multiplying by
a
the
y

coordinate of each point that is on the graph of
f
.
Compared to the graph of
( )
y
f x
=
, the graph of
( )
y
a f x
=
is:
stretched vertically if
1
a
>
;
compressed vertically if
0
1
a
<
<
.
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