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: