Section 6 5
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Section 6.5. Graph Square Root and Cube Root Functions. Radical Functions. Review: y = √x& y = 3 √x. New: y =a √(x-h) + k& y = a 3 √ (x – h) + k. Parent Function: y = √x. Domain: x > 0 Range: y > 0. Parent Function: y = 3 √x. Domain: all real numbers

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Section 6.5

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Section 6 5

Section 6.5

Graph Square Root and

Cube Root Functions


Radical functions

Radical Functions

  • Review:

  • y = √x& y = 3√x

  • New:

  • y =a √(x-h) + k& y = a3 √(x – h) + k


Parent function y x

Parent Function: y = √x

  • Domain: x > 0

  • Range: y > 0


Parent function y 3 x

Parent Function: y = 3√x

  • Domain: all real numbers

  • Range: all real numbers


Translations and shifts

  • y =a √(x-h) + k& y = a3√(x – h) + k

Translations and Shifts

  • a & k change the y-value

    • Take the original y-value

      • a(y) + k

  • h changes the x-value

    • Take the original x-value

      • x + h


Section 6 5

EXs.

  • y = 2 √x + 2

    • Change the y:

      • Double it and add 2

  • y = -1 √(x – 1) – 3

    • Change the y:

      • Take the opposite and subtract 3

    • Change the x:

      • Add 1


  • Points of importance y x

    Points of Importance: y = √x

    Points of Importance: y = 3√x


    Ex y 2 x 1 3

    EX. y = 2 √(x – 1) + 3

    • Now Plot!


    Now graph

    Now Graph…


    Ex y 3 3 x 7 6

    Ex. y = -33√(x + 7) - 6


    Section 6 5

    Note:

    • Label the parent and translation.

    • Make the parent graph be the dashed curve.

    • Show the table of values.


    Your turn

    Your Turn:

    • 449

    • A:3,7,11,17,19,29,41,43

    • B:6,10,16,32,44,47

    • C:5,15,19,20,30,50


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