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Section 6.5

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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  1. Section 6.5 Graph Square Root and Cube Root Functions

  2. Radical Functions • Review: • y = √x & y = 3√x • New: • y =a √(x-h) + k & y = a3 √(x – h) + k

  3. Parent Function: y = √x • Domain: x > 0 • Range: y > 0

  4. Parent Function: y = 3√x • Domain: all real numbers • Range: all real numbers

  5. 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

  6. 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

  7. Points of Importance: y = √x Points of Importance: y = 3√x

  8. EX. y = 2 √(x – 1) + 3 • Now Plot!

  9. Now Graph…

  10. Ex. y = -33√(x + 7) - 6

  11. Note: • Label the parent and translation. • Make the parent graph be the dashed curve. • Show the table of values.

  12. 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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