6-8 Graphing Radical Functions

Objective

To graph square root and other radical functions

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The formula A = π r 2 eh equals , pi r squared  shows that area is a quadratic function of the radius of a circle. The formula r = 1 π A r equals , fraction 1 , over square root of pi end fraction , square root of eh  shows that the radius of a circle is a square root function of the area.

Essential Understanding A square root function is the inverse of a quadratic function that has a restricted domain.

A horizontal line can intersect the graph of f ( x ) = x 2 f open x close equals , x squared  in two points—where f ( − 2 ) = f ( 2 ) , f open negative 2 close equals f open 2 close comma  for example. Thus, a vertical line can intersect the graph of f − 1 f super negative 1 end super  in two points. f − 1 f super negative 1 end super  is not a function because it fails the vertical line test.

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However, you can restrict the domain of f so that the inverse of the restricted function is a function.

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