radical expressions and radical functions objective: analyze graphs of rational functions and...

Radical Expressions and Radical Functions

Objective: Analyze graphs of rational functions and evaluate radical

expressions.

5 up 5left 5by stretch vert on x flip5,by stretch vert

51by n compressio horiz. 5by stretch horiz.

Example 1

Example 1

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• Find the domain of 185)( xxg

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• Find the domain of

• The domain of g(x) is

185)( xxg

518

185

0185

x

x

x

Transformations

Example 2

Example 2

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• For each function, describe the transformations applied to .xy

213 xy 42 xy

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• For each function, describe the transformations applied to .

• Vertical stretch of 3, Reflect on x-axis, down 2, to the right 1. horiz. Comp. of ½ up 4.

xy

213 xy 42 xy

Example 3

Example 3

Example 3

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• Find the inverse of . Then graph the function and its inverse together.

432 xxy

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• Find the inverse of . Then graph the function and its inverse together.

432 xxy

)4(30

43

43

2

2

2

xyy

yyx

xxy

)4(

3

1

xc

b

a

Try This

• Find the inverse of . Then graph the function and its inverse together.

432 xxy

)4(30

43

43

2

2

2

xyy

yyx

xxy

2

4253

2

16493

2

)4)(1(4)3(3 2 xxx

)4(

3

1

xc

b

a

Try This

• Find the inverse of . Then graph the function and its inverse together.

432 xxy

2

4253 x432 xxy

Example 4

Example 5

Example 5

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• Evaluate

1012523 2862

3

Try This

• Evaluate

1012523 2862

3

01010

10)5(2

262)4(6

226 2

2;063 xx

2down 4,right

3 ofstretch vert.5 up3,left

of comp. horiz. 21

yx

yx

yx

3

3

32

2

8)5(412

171027

1033 2

Homework

• Pages 525-526• 11-29 odd• 37-51 odd