The parent function is the simplest form of the type of function given.
g(x)=x2
The transformation being described is from
g(x)=x2 to f(x)
=x2.
g(x)=x2→f(x)=x2
Find the vertex form of f(x)=x2.
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y=x2
The horizontal shift depends on the value of h. The horizontal shift is described as:
f(x)=f(x+h) - The graph is shifted to the left
h units.
f(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:f(x)=f(x)+k - The graph is shifted up k units.
f(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
f(x)=−f(x).
Reflection about the x-axis: None
The graph is reflected about the y-axis when
f(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: None
Compare and list the transformations.
Parent Function:
g(x)=x2
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
