Transcript POWERPOINT JEOPARDY - St. Joseph School District

Factoring
Rational
Expressions
(1)
Rational
Expressions
(2)
Binomial
Theorem
Functions/In
verses
10
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30
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50
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50
Factoring- 10
Factor:
5x - 25x
2
Factoring– 10
• GCF
5x - 25x = 5x(x - 5)
2
Factoring- 20
• Factor:
25x - 36
2
Factoring – 20
• Binomial, difference of squares
25x - 36 = (5x + 6)(5x - 6)
2
Factoring - 30
• Factor:
2x - x - 3
2
Factoring – 30
Trinomial, ax2 type
2x + 2x - 3x - 3
2x(x + 1) - 3(x + 1)
(x + 1)(2x - 3)
2
Factoring - 40
• Factor:
8x +125
3
Factoring – 40
• Difference of Cubes
8x +125 = (2x + 5)(4x -10x + 25)
3
2
Factoring - 50
• Factor:
4x - 36x + 56
2
Factoring – 50
• GCF, then trinomial (x2 type)
4x - 36x + 56
2
4(x - 9x + 14)
4(x - 7)(x - 2)
2
Rational - 10
• Simplify the rational expression
3
16x y
2 2
20x y
Rational – 10
• Top and bottom are already as simple as they
can be, cancel things out.
3
16x y 4x
=
2 2
20x y
5y
Rational - 20
• Simplify the rational expression
3x - 6
2
x + 3 - 10
Rational – 20
• Top- GCF
• Bottom- Trinomial
(x2 type)
• Cancel
3x - 6
2
x + 3 - 10
3(x - 2)
=
(x - 2)(x + 5)
3
=
x+ 5
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
Rational (2)– 40
Rational (2)- 50
• Subtract the Rational Expressions
Rational (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 like
x7y2
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)
b)
c)
d)
e)
f)
Is it a function?
What is the domain?
What is the range?
Is it one-to-one?
Is it invertible?
What is the inverse?
Functions/Inverses– 10
• For {(-1,7),(3,4),(0,5),(-2,4)}
a)
b)
c)
d)
e)
Is it a function?---------------Yes
What is the domain?--------{-2,-1,0,3}
What is the range?----------{4,5,7}
Is it one-to-one?--------------No
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?----Yes
b) Is it one-to-one?---No
c) What is the domain?
(-infinity, infinity)
d) What is the range?
[-1,infinity)
e) Is it invertible?
No
Functions/Inverses- 30
Functions/Inverses– 30
Functions/Inverses- 40
• Find the inverse of: m(x)=2x2-5
Functions/Inverses–
2
m(x)
=
2x
-5
40
y = 2x - 5
2
x = 2y2 - 5
x + 5 = 2y2
x+ 5
2
=y
2
x+ 5
±
=y
2
x+ 5
m =±
2
-1
Functions/Inverses- 50
Function Composition:
Functions/Inverses– 50