 |
 |
 |
|
 |
|
 |
|
 |
|
 |
|
 |
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
Contents
Reflection
|
Reflection
Reflection
about the y-axis
Given
the graph y = f(x), a reflection about the y-axis is given by the graph
y = f (-x)
This
means the negative x-values of the original graph becomes positive in the
new graph. The same goes for the positive x-values. Co-ordinates on the
y-axis do not change.
 Example:
Sketch the graph of y = x3 - 3x2 + x - 4, and hence
sketch the graph of y = -x3 - 3x2 - x - 4 .
Solution:
Graph
of y = x3 - 3x2 + x - 4:
Graph
of y = -x3 - 3x2 - x - 4 :
On
inspection, y can be rewritten as:
y = (-x)3 - 3(-x)2 -(-x) - 4
= f (-x)
-->
Reflect about the y axis.
Reflection
about the x-axis
Given
the graph y = f(x), a reflection about the x-axis is indicated by
y = -f(x)
Negatives
y-values in the original graph become positive in the new graph and vice
versa. Co-ordinates on the x-axis do not change.
Example:
Sketch the graph of y = x2 - 2x + 3, and hence
sketch the graph of y = -x2 + 2x - 3 .
Solution:
Graph
of y = x2 - 2 x + 3:
Graph
of y = -x2 + 2 x - 3 :
On
inspection, y can be rewritten as
y = - (x2 - 2 x + 3)
= - f(x)
-->Reflect
about x-axis.
|
