2. 7.5 Graphing Square Root & Cube Root Functions By: L. Keali’i Alicea

3. First, let’s look at the graphs of a square root function. Always goes thru the points (0,0) and (1,a).

4. Now, let’s look at the graphs of a cube root function. Always goes thru the points (-1,-a), (0,0), and (1,a).

5. Generalization Always goes thru the points (0,0) and (1,a). Always goes thru the points (-1,-a), (0,0), and (1,a).

6. Ex: Graph Goes thru the points (0,0) and (1,a). Since a=-4, the graph will pass thru (0,0) and (1,-4)

7. Now, what happens when there are numbers added or subtracted inside and/or outside the radical? Step 1: Find points on the parent graph Step 2: Shift these points h units horizontally (use opposite sign) and k units vertically (use same sign).

8. Ex: Describe how to obtain the graph of from the graph of Shift all the points from To the right 2 and up 1.

9. Ex: Graph x y 0 1 2 4 9 6 Now, shift these points to the left 4 and down 1. x y -4 -1 -3 1 0 3 5 (x-value – 4) (y-value -1)

10. Ex: Graph x y -27 6 -8 4 -1 2 0 1 -2 8 -4 27 -6 Now, shift these points to the right 3 and up 2. (x-value + 3) (y-value + 2) x y -24 8 -5 6 2 4 3 2 4 0 11 -2 30 -4

11. Ex: State the domain and range of the functions in the last 2 examples. x-values y-values Domain: Range: Domain: Range: The graph doesn’t have a beginning or ending point. (Meaning all x & y-values are possible.) The graph has a beginning point of (-4,-1).

12. Assignment 7.5 A (1-6, 7-23 odd, 25-27) 7.5 A (1-6, 7-23 odd, 25-27)