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Understanding and Solving Radical Functions: Key Concepts and Examples

This guide explores fundamental concepts of radical functions, focusing on equations that include variables within the radicand. It outlines techniques to graph the functions and solve related equations by squaring both sides, highlighting the importance of checking for extraneous solutions. The document features step-by-step examples to illustrate solving methods using both algebraic approaches and graphing calculators. Homework exercises are also provided to reinforce learning and ensure mastery of the topic.

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Understanding and Solving Radical Functions: Key Concepts and Examples

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  1. 7.7 Radical Functions

  2. A radicalfunction has a variable in the radicand The Basic Graph Ex 1) Sketch left 2, up 3 We can transform this just like we do other graphs To solve an equation involving radicals, we need to “get rid of” the by squaring both sides. But, BEWARE! This often creates extra false solutions.  This is not optional! YOU MUST CHECK YOUR SOLUTIONS!

  3. *Hint: We usually try to have only 1 on a side of the equation. Ex 2) Solve and check each equation. a) Check! ()2()2 No! x = 14

  4. *Hint: We may have to square each side twice! b) Check! ()2()2 ()2()2 No! x = 5

  5. *Hint: We can do other roots, not just square roots! c) Check! ()3()3 x = 65 We can also solve using our graphing calculators – if it tells us to do so. Ex 3) Solve using your graphing calculator *Hint: Probably best to put everything on one side to have equal zero and find x-intercept(s) (graph on TV) –0.22

  6. Homework #707 Pg 374 #1, 5, 6, 10, 11, 15, 20, 22, 24, 28, 31, 32, 35, 37

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