Answer:
The parent function is the simplest form of the type of function given.
g
(
x
)
=
x
2
The transformation being described is from
g
(
x
)
=
x
2
to
h
(
x
)
=
−
3
x
2
.
g
(
x
)
=
x
2
→
h
(
x
)
=
−
3
x
2
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
h
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
h
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
h
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
h
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
In this case,
k
=
0
which means that the graph is not shifted up or down.
Vertical Shift: None
The graph is reflected about the x-axis when
h
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: Reflected
The graph is reflected about the y-axis when
h
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: Stretched
Compare and list the transformations.
Parent Function:
g
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: Reflected
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
image of graph
The parent function is the simplest form of the type of function given.
g
(
x
)
=
x
2
The transformation being described is from
g
(
x
)
=
x
2
to
h
(
x
)
=
−
3
x
2
.
g
(
x
)
=
x
2
→
h
(
x
)
=
−
3
x
2
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
h
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
h
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
h
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
h
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
In this case,
k
=
0
which means that the graph is not shifted up or down.
Vertical Shift: None
The graph is reflected about the x-axis when
h
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: Reflected
The graph is reflected about the y-axis when
h
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: Stretched
Compare and list the transformations.
Parent Function:
g
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: Reflected
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
image of graph
Step-by-step explanation:
so 
, 