LP4- odd.even...

LP4 odd.even functions(CASANO).notebook

1

December 13, 2017

Warm Up: If f(x) = x3 + 4:(a) find f-1(x)(b) Prove this is the inverse


2

December 13, 2017

Today I can identify even & odd functions.

If you substituted (-x) for all x-values, you get back the original function

look at the table in the calculator:


3

December 13, 2017

How to determine even, odd, or neither algebraically????

A function f is even iff each x in the domain of f..... f (x) = f (x).

Plug in x for each x & get original back!!!


4

December 13, 2017

If you substituted (-x) for all x-values, you get back the negation of the function



5

December 13, 2017


A function f is odd iff each x in the domain of f..... f (x) = f (x).

Plug in x for each x & factor out a 1!!!


6

December 13, 2017


If you substituted (-x) for all x-values, you neither get back the original nor negation of the function


7

December 13, 2017


If neither rule works, then it is neither even nor odd!!!


8

December 13, 2017

b


9

December 13, 2017

a


10

December 13, 2017

Determine whether each f(x) is even, odd, neither.

1) even2) odd3) neither4) neither5) neither6) neither


11

December 13, 2017

Determine whether each f(x) is even, odd, neither.

a) f(x) = x2-5

b) g(x) = x3-1

c) h(x) = 5x3-x

d) F(x) = |x|a) Evenb) Neitherc) Oddd) Even


12

December 13, 2017

a


13

December 13, 2017

c


14

December 13, 2017


15

December 13, 2017

Homework

: Finish an

ything

from the pa

cket that w

e didn't

get to in cl

ass.

Attachments

Mental Math Multiplication.ppt

Simplifying Rational Exponents.pdf

Mental Math

Multiplication

Number 1 - 8

3

2

1

1.)

6 x 7

2.)

8 x 4

3.)

7 x 8

4.)

9 x 4

5.)

13 x 4

6.)

11 x 13

7.)

15 x 11

8.)

12 x 11

Answers

1.) 42

2.) 32

3.) 56

4.) 36

5.) 52

6.) 143

7.) 165

8.) 132

SMART Notebook

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Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Simplifying Rational Exponents

Simplify.

1)

(

n4)

3

22)

(27

p6)

5

3

3)

(25

b6)−1.5

4)

(64

m4)

3

2

5)

(

a8)

3

26)

(9

r4)0.5

7)

(81

x12)1.25

8)

(216

r9)

1

3

Simplify. Your answer should contain only positive exponents with no fractional exponents in the

denominator.

9)

2

m2 ⋅

4

m

3

2 ⋅

4

m−2

10)

3

b

1

2 ⋅

b

4

3

11)

(

p

3

2 )−2

12)

(

a

1

2 )

3

2

-1-

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13)

2

x

−7

4

4

x

4

3

14)

4

x2

2

x

1

2

15)

3

x

−1

2 ⋅

3

x

1

2

y

−1

3

3

y

−7

4

16)

3

y

1

4

4

x

−2

3

y

3

2 ⋅

3

y

1

2

17)

(

m ⋅

m−2

n

5

3 )2

18)

(

a−1

b

1

3 ⋅

a

−4

3

b2)

2

19)

(

x

1

2

y−2

y

x

−7

4)

4

20)

(

x3

y2)

3

2

(

x−1

y

−2

3 )

1

4

21)

(

x

−1

2

y2)

−5

4

x2

y

1

2

22)

(

x

−1

2

y4)

1

4

x

2

3

y

3

2 ⋅

x

−3

2

y

1

2

-2-

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Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Simplifying Rational Exponents

Simplify.

1)

(

n4)

3

2

n6

2)

(27

p6)

5

3

243

p10

3)

(25

b6)−1.5

1

125

b9

4)

(64

m4)

3

2

512

m6

5)

(

a8)

3

2

a12

6)

(9

r4)0.5

3

r2

7)

(81

x12)1.25

243

x15

8)

(216

r9)

1

3

6

r3

Simplify. Your answer should contain only positive exponents with no fractional exponents in the

denominator.

9)

2

m2 ⋅

4

m

3

2 ⋅

4

m−2

32

m

3

2

10)

3

b

1

2 ⋅

b

4

3

3

b

11

6

11)

(

p

3

2 )−2

1

p3

12)

(

a

1

2 )

3

2

a

3

4

-1-

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13)

2

x

−7

4

4

x

4

3

x

11

12

2

x4

14)

4

x2

2

x

1

2

2

x

3

2

15)

3

x

−1

2 ⋅

3

x

1

2

y

−1

3

3

y

−7

4

3

y

17

12

16)

3

y

1

4

4

x

−2

3

y

3

2 ⋅

3

y

1

2

x

2

3

y

1

4

4

y2

17)

(

m ⋅

m−2

n

5

3 )2

n

10

3

m2

18)

(

a−1

b

1

3 ⋅

a

−4

3

b2)

2

a

1

3

b

14

3

a5

19)

(

x

1

2

y−2

y

x

−7

4)

4

x9

y12

20)

(

x3

y2)

3

2

(

x−1

y

−2

3 )

1

4

y

19

6

x

19

4

21)

(

x

−1

2

y2)

−5

4

x2

y

1

2

x

5

8

y3x2

22)

(

x

−1

2

y4)

1

4

x

2

3

y

3

2 ⋅

x

−3

2

y

1

2

x

17

24

y

-2-

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SMART Notebook

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