5.5 Graphing radical functions

Ideas in this lesson

Square-root and cube-root parent graphs

The square-root parent has an endpoint at the origin. The cube-root parent extends across all real inputs.

Transform radical graphs

Locate the horizontal and vertical shifts, then apply any vertical stretch or reflection to the parent outputs.

Domain and range

For a square-root graph, use the radicand restriction and the sign of the outside coefficient. A shifted cube-root graph has all real inputs and outputs.

Intercepts and graph interpretation

Set the output equal to zero for horizontal intercepts. Set the input equal to zero for a vertical intercept only if zero belongs to the domain.