Section 5.1.2

Rational Functions

Lesson Objective:

Students will:

• Transform functions in the form

into shifts of

• Be able to simplify complicated rational expressions.

ax by

x c+

=-1

.yx

=

Lesson Objective:

Students will:

• Review negative exponents.

• Be able to simplify complicated rational expressions.

Definitions

Rational Function: the ratio of two functions of the form:

( )( ) , ( ) 0

( )g x

f x h xh x

= ¹

Example of a Rational Function

2

32 3

( )2

xf x

x x

+=

- -

g(x)

h(x)

More Examples

21

( )2 5

f xx x

=+ +

2

3 22( )

x xp x

x-

=

Not Examples

1( )f x

x=

2( )

1

xp x

x=

+

5-14:

a: Write as a mixed number.

31

17

2017

5-14:

b: Illustrate the technique shown in (a) on the

number .

52

7

197

5-16:

Use the technique in 5-14 to change

3( ) 1

1g x

x= +

-

2( )

1x

g xx

+=

-

5-16:

a: Sketch g(x) using transformations.

3( ) 1

1g x

x= +

-

5-16:

b: Use the technique to change2 5

( )3

xh x

x-

=-

1( ) 2

3h x

x= +

-

Definitions

Negative Exponents:

1, 0n

na a

a- = ¹

Multiplication of Exponents

0

0

1

1

n n

n n

a a

a a

a

-

- +

=

=

=

g

Eliminate Negative Exponents

Multiply the rational expression

by 1 or .n

n

aa

Example

1 2

( )x y

f xx y

- -+=

+

5-19: Simplify each of the following expressions using concept of removing negative exponents.

a:1 2

2 1 2

x y yx y xy

-

- -

++

3 2 2

3 31xy x y

x y+

+

5-19:

b:

2 6

3

11x y

xy+

+

2 3 3

3

x y yy x

-

-

++

Assignment

Pg 235  #5-27 TO 5-28

Assignment

Pg 235  #5-22 TO 5-26