7.5 Graphing Square Root

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7.5 Graphing Square Root Cube Root Functions

• p. 431

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• 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?

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First, lets look at the parent graphs.
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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).
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Generalization
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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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.
(-12, 11) (02,01) (12,11) (1,2)
(2,1) (3,2)
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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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OrJust Graph
by picking values
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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Orjust graph
By picking values that will combine to make the
value under the radical a real number using the
3rd root.

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

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Assignment
Page 434, 15-21, 22-44 even