1. 7.5 Graphing Square Root & Cube Root Functions

2. What do the graphs of and look like?
What is the standard equation for a square root or cube root whose center has been translated?
How do you graph a square root function?
How do you graph a cube roof function?
What is domain & range?

3. First, let’s look at the parent graphs.

4. Now, what happens when there is a number in front of the radical?
* Notice the graph goes thru the points (0,0) and (1,2).
* Notice the graph goes thru the points (-1, 3), (0,0), & (1,-3).

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.
(−1+2, 1+1) (0+2,0+1) (1+2,1+1)
(1,2) (2,1) (3,2)

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

10. Or…Just Graph
by picking values
x y

11. Ex: Graph Now, shift these points to the right 3 and up 2. x y -27 6
(x-value + 3)
(y-value + 2)
Now, shift these points to the right 3 and up 2.
x y -2 -4
x y 4 2 -2

12. Or…just graph
By picking values that will combine to make the value under the radical a real number using the 3rd root.
x y 4 2 -2

13. 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).

14. Helpful Hints (h,k) is where the graph will begin.
(h,k) is where the graph will change directions.

15. What do the graphs of and look like?
Half of a parabola and a s-shaped graph.
What is the standard equation for a square root or cube root whose center has been translated?
How do you graph a square root function?
Find the new beginning point from (h,k) and then pick points to plot.
How do you graph a cube roof function?
Find the new center point from (h,k) of the S curve and then pick points to the left and to the right to plot.
What is domain & range?
Domain are the x values for the graph and the range are the y values for the graph

16. Assignment
Page 434, 15-21, even