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: