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 moves?up for positive?values of?a?and?down for negative?values of?a
  • The?x-coordinates stay the same

• • 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