The transformation from the first equation to the second one can be found by finding
a
a
,
h
h
, and
k
k
for each equation.
y
=
a
|
x
−
h
|
+
k
y
=
a
|
x
-
h
|
+
k
Factor a
1
1
out of the absolute value to make the coefficient of
x
x
equal to
1
1
.
y
=
|
x
|
y
=
|
x
|
Factor a
1
1
out of the absolute value to make the coefficient of
x
x
equal to
1
1
.
y
=
|
x
|
−
4
y
=
|
x
|
-
4
Find
a
a
,
h
h
, and
k
k
for
y
=
|
x
|
−
4
y
=
|
x
|
-
4
.
a
=
1
a
=
1
h
=
0
h
=
0
k
=
−
4
k
=
-
4
The horizontal shift depends on the value of
h
h
. When
h
>
0
h
>
0
, the horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
h
units.
g
(
x
)
=
f
(
x
−
h
)
g
(
x
)
=
f
(
x
-
h
)
- The graph is shifted to the right
h
h
units.
Horizontal Shift: None
