Function transformations

Explain how input and output changes affect graph position and shape.

Meaning

Transformations represent new functions by shifting, reflecting, or scaling existing graphs. Changing the input and adding to the output move a graph differently.

Example

Shifting right 3 and up 2 gives The vertex moves from to To reproduce the old height at input u in the new location x=u+3, substitute u=x−3. Thus the minus sign inside the function moves points three units to the right. shifts right. Do not infer leftward movement just from the minus sign; check which input gives an original output.

Practice for this concept

Scope and references

Topics

Translations, reflections, stretches and compressions, absolute-value graphs

Learning goal

Explain how input and output changes affect graph position and shape.

Helpful background

Explore coordinates and the original input–output relationship.