Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

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Presentation transcript:

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Algebraically A function is even if A function is odd if All of the exponents of the variable are even. A function is odd if All of the exponents of the variable are odd. The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither. A function is neither if The exponents are a mixture of odd and even

All constants really have a x0 BEWARE OF CONSTANTS All constants really have a x0 The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

x0 is EVEN!! The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Graphically A function is even if A function is odd 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 easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither. 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? Ex. 1 Algebraically 1 ODD

Even, Odd or Neither? Ex. 2 Algebraically x0 EVEN

Even, Odd or Neither? Ex. 3 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

If the dots shown are part of an even function, what points are also on the function?

If the dots shown are part of an odd function, what points are also on the function?