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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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Presentation Transcript
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
slide6
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

slide12
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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