103 Graphs of Radical Equations

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10-3 Graphs of Radical Equations
If you do not have a calculator, please get one
from the back wall! The Chapter 10 test is a NON
calculator test!
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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A square root function is defined by the equation
A function is a rule that establishes a
relationship between two quantities, called the
input and the output.
The collection of all input values is the domain
of the function and the collection of all output
values is the range of the function.
When finding the domain and range of a square
root function, remember a square root is defined
only when the radicand is non-negative.
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Graph .
Set up a table of values.
What is the domain of this function? (What
values should you choose for x?)
Why cant you choose a negative value?
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Graph .
Set up a table of values.
Graph these points.
What is the domain of this function? (What
values should you choose for x?)
What is the range of this function? (What values
will be generated for y?)
Domain is all real numbers gt 0.
Range is all real numbers gt 0.
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Graph .
Set up a table of values.
y






x
Calculate another point. Can you find one
without using your calculator?
You need to find the endpoint of the graph. To
find the endpoint set the expression under the
radical equal to zero and solve for x. That will
give the x coordinate of the endpoint.
Connect the points with a smooth curve.
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What is the endpoint for the graph
?
Do NOT use a calculator for the rest of the
lesson!
To find the endpoint set the expression under the
radical equal to zero and solve for x. That will
give the x coordinate of the endpoint
Endpoint at (0,0)
What value is generated when you calculate the
value of y?
Calculate another point without using your
calculator?
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What is the endpoint for the graph
?
Endpoint at (0,0)
What is the domain and range of the graph?
Domain is all real numbers lt 0.
Range is all real numbers gt 0.
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What is the endpoint for the graph
?
Endpoint at (-5,0)
What is the domain and range of the graph?
Since you want the radicand to be zero, set the
expression under the radical equal to zero and
solve for x.
Domain is all real numbers gt -5.
Range is all real numbers gt 0.
What value is generated when you calculate the
value of y?
Choose another value for x that you can easily
calculate the y value in your head?
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What is the endpoint for the graph
?
Endpoint at (-2,0)
Since you want the radicand to be zero, set the
expression under the radical equal to zero and
solve for x.
What is the domain and range of the graph?
Domain is all real numbers gt -2.
Range is all real numbers gt 0.
What value is generated when you calculate the
value of y?
Choose another value for x that you can easily
calculate the y value in your head?
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Graph
Example 1
Example 2
Example 3
To graph functions involving square roots you
must find the endpoint!
Copy all of the above on you paper before you
begin to graph.
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Example 1 Graph
Your graph must include the endpoint. Set up a
table of values.
Endpoint at (0,0)
Where is the endpoint?
What is the domain and range of the graph?
Domain is all real numbers gt 0.
Range is all real numbers lt 0.
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Example 1 Graph
Your graph must include the endpoint. Set up a
table of values.
x





y
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Example 2 Graph
Your graph must include the endpoint. Set up a
table of values.
Endpoint at (0,3)
Where is the endpoint?
What is the domain and range of the graph?
Domain is all real numbers gt 0.
Range is all real numbers gt 3.
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Example 2 Graph
Your graph must include the endpoint. Set up a
table of values.





x
y
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Your graph must include the endpoint. Set up a
table of values.
Example 3 Graph
Endpoint at (-3,0)
Since you want the radicand to be zero, set the
expression under the radical equal to zero and
solve for x.
What is the domain and range of the graph?
Domain is all real numbers gt-3.
Range is all real numbers gt 0.
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Your graph must include the endpoint. Set up a
table of values.
Example 3 Graph




x
y
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Homework
10-A11 Page 544 33-38 and Page 547 19.