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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

All constants really have a x0

x0 is EVEN!!

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, Odd or Neither?

Algebraically

1

ODD

Even, Odd or Neither?

Ex. 2

Algebraically

x0

EVEN

Even, Odd or Neither?

Graphically

EVEN

Even, Odd or Neither?

Ex. 4

Graphically

Neither

Even, Odd or Neither?

1

x0

EVEN

ODD

Even, Odd or Neither?

x0

ODD

ODD

Even

Even, Odd or Neither?

1

1 x0

neither

ODD

neither

Even, Odd or Neither?

EVEN

ODD

Even, Odd or Neither?

EVEN

Neither

ODD

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

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

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

Complete the sheet and turn in for a grade.