Radical Functions and Equations

Radical Functions and Equations

l  A radical function is a function that has a variable in the radicand.

l  You can apply the same transformations to the graphs of radical functions as you can to polynomial functions.

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Radical Parent functions

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Transformations

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Domain:______Domain:______Domain:______

Range:______Range:______Range:______

Applying the transformations

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Radical Equations

•  To solve a radical equation that has only one variable in the radicand, isolate that term on one side of the equation. If the index is 2, then ______both sides of the equation.

First, isolate the radical :

Then, Square both sides (FOIL!) : ______=______

Simplify and set equal to zero : ______

Factor: ______

Solve: ______

Be careful! The new equation you created when you squared both sides might have ______solutions!

Always check your solutions. In the example problem, only one solutions works. Make sure your answers are given as

solutions sets. The answer would be: ______.

Try: Try:

More Solving Radical Equations:

l  A radical equation may contain two radical expressions with an index of 2.

l  To solve these, rewrite the equation with ______isolated on one side of the equals sign.

l  Then, ______both sides.

l  If a variable remains in a radicand, you must ______the squaring process.

Try: Try:

·  Radical equations with ______greater than 2 can be solved using similar techniques.

·  After isolating the term containing the radical, raise each side of the equation to the

______equal to the index of the radical.

Try: