7.5 Graphing Square Root

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7.5 Graphing Square Root Cube Root Functions

• By L. Kealii Alicea

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First, lets look at the graphs of a square root
function.
Always goes thru the points (0,0) and (1,a).
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Now, lets look at the graphs of a cube root
function.
Always goes thru the points (-1,-a), (0,0), and
(1,a).
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Generalization
Always goes thru the points (-1,-a), (0,0), and
(1,a).
Always goes thru the points (0,0) and (1,a).
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Ex 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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Ex 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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Ex 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
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Ex 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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Ex State the domain and range of the functions
in the last 2 examples.
y-values
x-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).
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Assignment

• 7.5 A (1-6, 7-23 odd, 25-27)