Graph Transformations 1
The graph of modified functions can often be deduced from simple geometrical transformations of the graph of the original function. To deduce the transformation, we often consider how a few points on the graph are modified from the original graph and then extrapolate.
We explain which modified function corresponds to the appropriate transformation on the graph of $$f$$. $$a\ne 0$$ is a fixed number.
- Horizontal translation of $$a$$: $$f(x-a)$$
- Vertical translation of $$a$$: $$f(x)+a$$
- Horizontal scaling of ratio $$1/a$$: $$f(ax)$$. It is a stretch or dilation if $$\vert a\vert \lt 1$$ and a compression if $$\vert a\vert \gt 1$$.
- Vertical scaling of ratio $$1/a$$: $$af(x)$$
- Horizontal reflection (along vertical axis): $$f(-x)$$
- Vertical reflection (along horizontal axis): $$-f(x)$$
- Rotation of angle $$\pi$$ about the origin:$$-f(-x)$$