10-3C 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-HillLinda Stamper

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.

Graph. Set up a table of values. What is the domain of this function? (What values should you choose for x?) Why can’t you choose a negative value?

Graph. Set up a table of values. What is the range of this function? (What values will be generated for y?) Range is all real numbers > 0. Domain is all real numbers > 0. What is the domain of this function? (What values should you choose for x?) Graph these points.

Graph. Set up a table of values. x y Calculate another point. Can you find one without using your calculator? Connect the points with a smooth curve. 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.

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 What is the endpoint for the graph ? Endpoint at (0,0) What value is generated when you calculate the value of y? Calculate another point without using your calculator?

What is the endpoint for the graph ? Endpoint at (0,0) Domain is all real numbers < 0. Range is all real numbers > 0. What is the domain and range of the graph? Graph these points.

What is the endpoint for the graph ? Endpoint at (-5,0) 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? Since you want the radicand to be zero, set the expression under the radical equal to zero and solve for x. Range is all real numbers > 0. Domain is all real numbers > -5. What is the domain and range of the graph? Graph these points.

Since you want the radicand to be zero, set the expression under the radical equal to zero and solve for x. What is the endpoint for the graph ? Endpoint at (-2,0) What value is generated when you calculate the value of y? Domain is all real numbers > -2. Choose another value for x that you can easily calculate the y value in your head? Range is all real numbers > 0. What is the domain and range of the graph? Graph these points.

Example 1 Graph Example 2 Example 3 Copy all of the above on you paper before you begin to graph. To graph functions involving square roots you must find the endpoint!

Example 1 Graph Your graph must include the endpoint. Set up a table of values. Range is all real numbers < 0. Domain is all real numbers > 0. What is the domain and range of the graph? Endpoint at (0,0) Where is the endpoint?

Example 1 Graph Your graph must include the endpoint. Set up a table of values. x y

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

Example 2 Graph Your graph must include the endpoint. Set up a table of values. x y

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

Example 3 Graph Your graph must include the endpoint. Set up a table of values. x y

10-A12 Page 544 # and Page 547 # 1–9.