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 = a 3 √(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. 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 y =a √(x-h) + k& y = a 3 √(x – h) + k

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 x0149 y0123 Points of Importance: y = 3 √x x018-8 y012-2

8. EX. y = 2 √(x – 1) + 3 Now Plot! x0149 y0123 New x: x + 112510 New y: 2y + 33579

9. Now Graph…

10. Ex. y = -3 3 √(x + 7) - 6 x018 y012 New x: x - 7-7-61 New y: -3y - 6-6-9-12

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

13. 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