Even and Odd Functions
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Even and Odd Functions. Algebraically. A function is even if. All of the exponents of the variable are even. A function is odd if. All of the exponents of the variable are odd. A function is neither if. The exponents are a mixture of odd and even. BEWARE OF CONSTANTS.

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Even and Odd Functions

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Even and odd functions

Even and Odd Functions


Even and odd functions

Algebraically

A function is even if

All of the exponents of the variable are even.

A function is odd if

All of the exponents of the variable are odd.

A function is neither if

The exponents are a mixture of odd and even


Even and odd functions

BEWARE OF CONSTANTS

All constants really have a x0


Even and odd functions

x0 is EVEN!!


Even and odd functions

Graphically

A function is even if

The graph reflects across the y-axis

(means you can fold it hotdog style and it would match up).

A function is odd if

The graph has 180 rotational symmetry about the ORIGIN

(means you could turn it upside-down & it would still look the same...it must go through the origin).


Even and odd functions

Even, Odd or Neither?

Ex. 1

Algebraically

1

ODD


Even and odd functions

Even, Odd or Neither?

Ex. 2

Algebraically

x0

EVEN


Even and odd functions

Even, Odd or Neither?

Ex. 3

Graphically

EVEN


Even and odd functions

Even, Odd or Neither?

Ex. 4

Graphically

Neither


Even and odd functions

Even, Odd or Neither?

1

x0

EVEN

ODD


Even and odd functions

Even, Odd or Neither?

x0

ODD

ODD

Even


Even and odd functions

Even, Odd or Neither?

1

1 x0

neither

ODD

neither


Even and odd functions

Even, Odd or Neither?

EVEN

ODD


Even and odd functions

Even, Odd or Neither?

EVEN

Neither

ODD


Texting response

Texting response…


Even and odd functions

Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.


Even and odd functions

Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.


Even and odd functions

Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.


Skills check

Skills Check

Complete the sheet and turn in for a grade.


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