FactoringRational

Expressions (1)

Rational Expressions

(2)

Binomial Theorem

Functions/Inverses

10 10 10 10 10

20 20 20 20 20

30 30 30 30 30

40 40 40 40 40

50 50 50 50 50

Factoring- 10

Factor:

Factoring– 10

• GCF

Factoring- 20

• Factor:

Factoring – 20

• Binomial, difference of squares

Factoring - 30

• Factor:

Factoring – 30

Trinomial, ax2 type

Factoring - 40

• Factor:

Factoring – 40

• Difference of Cubes

Factoring - 50

• Factor:

Factoring – 50

• GCF, then trinomial (x2 type)

Rational - 10

• Simplify the rational expression

Rational – 10

• Top and bottom are already as simple as they can be, cancel things out.

Rational - 20

• Simplify the rational expression

Rational – 20

• Top- GCF• Bottom- Trinomial (x2 type)• Cancel

Rational - 30

• Multiply the rational expressions

Rational – 30

• Factor top and bottom, put together, cancel

Rational - 40

• Multiply the rational expressions

Rational – 40 1: Factor all numerators and denominators:

2: Cancel all common factors:

3: Multiply the denominators and numerators:

Rational - 50

Rational – 50

• Flip the second one• Factor the top• Factor the bottom• Cancel

Rational (2) - 10

• Divide the rational expression

Rational (2) – 10 • Flip the second one,• Factor the top• Factor the bottom• Cancel

Rational (2) - 20

• Add the rational expression

Rational (2)– 20

Rational (2)- 30

• Subtract the rational expression

Rational (2)– 30

Rational (2)- 40

• Add the rational expression

Ratio

nal (

2)–

40

Rational (2)- 50

• Subtract the Rational Expressions

Ratio

nal (

2)–

50

Binomial Theorem- 10

• Fill in the missing pieces of Pascal’s triangle– (Rewrite this whole chunk on your white board)

Binomial Theorem– 10

Binomial Theorem- 20

• Use Binomial Expansion to Expand:(x+2)5

Binomial Theorem– 20

Binomial Theorem- 30

• Use the binomial theorem to expand:

(2x – 5y)7

Binomial Theorem– 30

128x7 – 2240x6y + 16800x5y2 – 70000x4y3

+ 175000x3y4 – 262500x2y5+ 218750xy6

– 78125y7

Binomial Theorem- 40

Binomial Theorem– 40

Third term is likex7y2

Binomial Theorem- 50

Binomial Theorem– 50

5th term would be like x8y4

Functions/Inverses- 10

• For {(-1,7),(3,4),(0,5),(-2,4)}a) Is it a function?b) What is the domain?c) What is the range?d) Is it one-to-one?e) Is it invertible?f) What is the inverse?

Functions/Inverses– 10

• For {(-1,7),(3,4),(0,5),(-2,4)}a) Is it a function?---------------Yesb) What is the domain?--------{-2,-1,0,3}c) What is the range?----------{4,5,7}d) Is it one-to-one?--------------Noe) Is it invertible?----------------No

(The inverse is not a function since it is not one to one)

f) What is the inverse?--------

{(7,-1),(4,3),(5,0),(4,-2)}

Functions/Inverses- 20

For the graph state the following:a)Is it a function?b)Is it one-to-one?c)What is the domain?d)What is the range?e)Is it invertible?

Functions/Inverses– 20 For the graph state the following:a)Is it a function?----Yesb)Is it one-to-one?---Noc)What is the domain?

(-infinity, infinity)d) What is the range?

[-1,infinity)e) Is it invertible?

No

Functions/Inverses- 30

Func

tions

/Inv

erse

s– 3

0

Functions/Inverses- 40

• Find the inverse of: m(x)=2x2-5

Functions/Inverses– 40

Functions/Inverses- 50

Function Composition:

Functions/Inverses– 50