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Graphing Radical Functions: Transformations and Inverse Functions

Learn how to graph and transform radical functions, and explore the concept of inverse functions. Practice identifying domain and range of radical functions.

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Graphing Radical Functions: Transformations and Inverse Functions

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  1. Radical Functions Essential Questions • How do we graph radical functions and inequalities? • How do we transform radical functions by changing parameters? Holt McDougal Algebra 2 Holt Algebra 2

  2. Recall that exponential and logarithmic functions are inverse functions. Quadratic and cubic functions have inverses as well. The graphs below show the inverses of the quadratic parent function and cubic parent function.

  3. A radical function is a function whose rule is a radical expression. A square-root function is a radical function involving . The square-root parent function is . The cube-root parent function is .

  4. Comparing Radical Graphs Describe how to obtain the graph of g from the graph of f. 3 units up Vertical shift: Horizontal shift: 5 units to the left 4 units down Vertical shift: Horizontal shift: 1 units to the right 6 units up Vertical shift: Horizontal shift: 1 units to the left

  5. Graphing Radical Functions Graph the radical function and identify the domain and range. Up 4 times as fast Domain: Range:

  6. Graphing Radical Functions Graph the radical function and identify the domain and range. Up 2 times as fast Horizontal shift: 3 units to the left Domain: Range:

  7. Graphing Radical Functions Graph the radical function and identify the domain and range. 3 times as fast Horizontal shift: 2 units to the right Domain: Range:

  8. Graphing Radical Functions Graph the radical function and identify the domain and range. opposite 2 times as fast Horizontal shift: 1 unit to the left Vertical shift: 2 units down Domain: Range:

  9. Graphing Radical Functions Graph the radical function and identify the domain and range. Left 2 times as fast Domain: Range:

  10. Graphing Radical Functions Graph the radical function and identify the domain and range. opposite normal Horizontal shift: 2 units to the right Vertical shift: 1 unit up Domain: Range:

  11. Lesson 7.1 Practice A

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