7.5 Graphs Radical Functions

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7.5 Graphs Radical Functions
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Graph of the Square Root
x y
-1 i
0 0
1 1
4 2
Note We cannot graph imaginary numbers on the
coordinate plane. Therefore, the graph stops at
x 0.
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Graph of the Cube Root
x y
-4 -1.59
-1 -1
0 0
1 1
4 1.59
Note Since the index number is odd, we can
graph the function for all x values. Therefore,
the domain is all reals.
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The General Equation
The general form of the square root function is
The cube root function is
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Add a positive positive number to x.
Shift left h.
Add a negative number to x.
Add a positive number to the radical.
Add a negative number to the radical.
Shift right h.
Up k.
Down k.
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Add a positive positive number to x.
Shift left h.
Add a negative number to x.
Add a positive number to the radical.
Add a negative number to the radical.
Shift right h.
Up k.
Down k.
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Changing a
a is greater than 1
a is greater than 0 and less than 1.
a is less than 0.
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Problems
Describe how to obtain the graph of g from the
graph of f.
Shift left 5 units.
Reflect in y 0, shift down 10 units.
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Problems
State the domain and range.
x gt -6, y gt 0
x, y all real numbers