10-3C Graphs of Radical Equations

If you do not have a calculator, please get one from the backwall! The Chapter 10 test is a NON calculator test!

Algebra 1 Glencoe McGraw-Hill Linda Stamper

A square root function is defined by the equation xy 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 . x2y

x2y y,xx

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 . x2y

x2y y,x

00

02y

)0,0(

12

12y

2,12

8.222y

8.2,2 3

5.332y

5.3,3

44

42y

4,4

x

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 . x2y

x2y y,x

00

02y

)0,0(

12

12y

2,12

8.222y

8.2,2 3

5.332y

5.3,3

44

42y

4,4

x

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 ? xy

xy y,x

0

1

4

x

Endpoint at (0,0)

What value is generated when you calculate the value of

y?

00y

)0,0(

1

1y

)1,1(

24

4y

)2,4(

9

39

9y

)3,9( Calculate

another point without using

your calculator?

What is the endpoint for the graph ? xy

xy y,x

0

1

4

x

Endpoint at (0,0)

00y

)0,0(

Domain is all real numbers < 0.Range is all real numbers > 0.

1

1y

)1,1(

24

4y

)2,4(

9

39

9y

)3,9(

What is the domain and range of the graph?

Graph these points.

What is the endpoint for the graph ? 5xy

5xy y,x

5

1

4

x

Endpoint at (-5,0)

What value is generated when you calculate the value of

y?

)0,5(

055y

24

51y

)2,1(

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.

4

11

54y

)1,4(Domain is all real numbers > -5.

39

54y

)3,4(

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 ? 4x2y

4x2y y,x

2

0

x

Endpoint at (-2,0)

What value is generated when you calculate the value of

y?

)0,2(

Domain is all real numbers > -2.

0

422y

)2,0(

Choose another value for x that you can

easily calculate the y value in your head?

Range is all real numbers > 0.

24

402y

What is the domain and range of the graph?

6

)4,6(

Graph these points.

4

16

412

462y

Example 1

x2y

Graph

Example 2

3xy

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!

3xy

Example 1 Graph

.x2y

x2y y,x

00

02y

)0,0(

12

12y

2,12

8.222y

8.2,2 4

442y

4,4

96

92y

6,9

x

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

.x2y

x2y y,x

00

02y

)0,0(

12

12y

2,12

8.222y

8.2,2 4

442y

4,4

96

92y

6,9

x

Your graph must include the endpoint. Set up a table of values.

x

y

••••

•

Example 2 Graph

.3xy

3xy y,x

0)3,0(

1 4,1

2

4.4,2 4

5,4

9 6,9

x

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?

330y

431y

4.432y

534y

639y

Example 2 Graph

.3xy

3xy y,x

0)3,0(

1 4,1

2

4.4,2 4

5,4

9 6,9

x

Your graph must include the endpoint. Set up a table of values.

330y

431y

4.432y

534y

639y

x

y

•• • • •

Example 3 Graph

.3xy

3xy y,x

3)0,3(

2 1,2

1

2,1

6

9,6

13 4,13

x

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.

0

33y

Endpoint at (-3,0)

1

32y

2

31y

9

36y

4

313y

What is the domain and range of the graph?

Example 3 Graph

.3xy

3xy y,x

3)0,3(

2 1,2

1

2,1

6

3,6

13 4,13

x

Your graph must include the endpoint. Set up a table of values.

0

33y

1

32y

2

31y

3

36y

4

313y

x

y

•• • •

10-A12 Page 544 # 33-38 and Page 547 # 1–9.