6.5 Graph Square Root

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6.5 Graph Square Root Cube Root Functions
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First, lets 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.
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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.
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Notice
Always goes thru the points (0,0) and (1,a).
Always goes thru the points (-1,-a), (0,0), and
(1,a).
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Graph
Goes thru the points (0,0) and (1,a). Since a-4,
the graph will pass thru (0,0) and (1,-4)
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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).
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Describe how to obtain the graph of
from the graph of
Shift all the points from To the right 2 and up
1.
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Graph
(x-value 4)
(y-value -1)
Now, shift these points to the left 4 and down 1.

• x y
• 0 0
• 2
• 4
• 9 6

x y -4 -1 -3 1 0 3 5 5
9
Graph
(x-value 3)
(y-value 2)
Now, shift these points to the right 3 and up 2.

• x y
• -27 6
• -8 4
• -1 2
• 0 0
• -2
• -4
• 27 -6

• x y
• -24 8
• -5 6
• 4
• 2
• 0
• -2
• 30 -4

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State the domain and range of the functions in
the last 2 examples.
x-values
y-values
Domain Range
Domain Range
The graph doesnt have a beginning or ending
point. (Meaning all x y-values are possible.)
The graph has a beginning point of (-4,-1).