1. 6.5 Graph Square Root & Cube Root Functions

2. First, let’s look at the graphs.
(27,3)
(16,4)
(8,2)
(9,3))
(1,1)
(4,2)
(-1,-1)
(-8,-2)
(-27,-3)
Think of these as “parent” functions.

3. Now, what happens when there is a multiplier in front of the radical?
(16,8)
(-27,9)
(9,6)
(8,2)
(27,3)
(4,4)
(1,2)
(16,4)
(-27,-3)
(9,3)
(27,-9)
(4,2)
(8,-6)
(1,1)
Notice the “parent” has been “doubled” for each x-value. Can you guess what the graph of
Notice the “parent” has “reversed” sign and tripled for each x-value.

4. Notice Always goes thru the points (0,0) and (1,a).
Always goes thru the points (-1,-a), (0,0), and (1,a).

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

6. 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).

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

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

9. Graph Now, shift these points to the right 3 and up 2. x y -27 6 -8 4
(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

10. 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).