Reflections
Definition
Reflections are a type of transformation, allowing for the graph to be flipped across a line to create a mirror image on the other side.
Reflections are similar to dilations, since it is, with respect to the function , .
Note
In Mathematics Advanced, only reflections about the x and y-axis will be explored.
Vertical Reflections
Vertical reflections are reflections about the x-axis. This is when every y-value is flipped.
Let .
| x | 0 | 1 | 2 |
|---|---|---|---|
| y | 0 | 1 | 8 |
Now, reflect vertically. This should now return as .
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 8 | 1 | 0 | -1 | -8 |
Tip
In vertical reflections, the y-intercept of the function CAN change. For instance, let . The y-intercept of this function is (0, 1). If it was vertically reflected ()…
The y-intercept is now (0, -1).
Horizontal Reflections
Horizontal reflections are reflections about the y-axis. This is when every x-value is flipped.
Let .
| x | 0 | 1 | 2 |
|---|---|---|---|
| y | 0 | 1 | 8 |
Now, reflect horizontally. This should now return as . Thus, its values are the same (since it is an even function).
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 8 | 1 | 0 | -1 | -8 |
Tip
Horizontal reflections CANNOT change the y-intercept because the y-values do not change (only the x-values do).
Combined Reflections
To combine reflections, see below.