What are graph transformations?
- When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations
- With a translation the shape, size, and orientation of the graph remain unchanged – the graph is merely shifted (up or down, left or right) in the xy plane
- A particular translation (how far left/right, how far up/down) is specified by a translation vector:
What do I need to know about graph translations?
- The graph of is a vertical translation of the graph by the vector
- The graph moves up for positive values of a and down for negative values of a
- The x-coordinates stay the same
- The graph of is a horizontal translation of the graph by the vector
- The graph moves left for positive values of a and right for negative values of a
- The y-coordinates stay the same
- Any asymptotes of f(x) are also translated. If an asymptote is parallel to the direction of translation, however, it will not be affected