Connection between even and odd numbers and functions | Algebra II | Khan Academy

[@alexrox321]

You are my favourite lecturer, end of. Please lecture at my university. I beg you.

[@IsaacC20]

The way to determine whether f(x) is even or odd is to see whether the the set of ordered pairs of the function fits the criteria: 1) A function is even if f(x) = f(-x). 2) A function is odd if f(-x) = -f(x).

[@cosmosgato]

Are all even functions a repeated series or combination of x^n n being even? Similarly for odd.

[@totasalam7060]

thank you so much

[@kawaiipickle479]

I love you so much !!!!

[@bradleywilliambusch5198]

Equal Exponential Rule If both x and y are negative integers: -1*-1/x^y=1/(-1/x^x) If both x any y are positive integers: -1/x^y=-1*1/(-1/x^x) Opposite Exponential Rule The negative integer is expressed as the exponent x^y=1/x^x The negative integer is expressed as the exponent -1*x^y=-1/x^x The algebra is conserved, but there are the additional rules that the opposite equations cannot be expressed in the order of a number line (i.e. the negative integer must be expressed as the exponent for the opposite check), and that for the equal check if both numbers are negative integers they must be expressed as -1/x^y=-1*1/(-1/x^x) so that if both integers are positive they be expressed as -1/x^y=-1*1/(-1/x^x) or the opposite checks break down.

[@420hassam]

do vid on absolute-valued function

[@aashaysatheas]

Maybe. Even number of flips=>Odd function Odd number of flips=>Even function

[@DuckQuickly]

It seemed to me that even functions have only even powers of x in their Taylor series and odd functions have only odd powers. Functions that are neither even nor odd have a mixture of both. I could be wrong, though.

[@andresduarte010]

what about functions that are both even an odd? are there any?

[@thesocialgod]

@Mikej1592 Oh yeah right. :P It should be -7 :D I didn't notice that. :P I was just brushing up the notes at khan academy for my exam which was today and it was alright. The maths part was good. :D

[@ncquake24]

@andresduarte010 if it has an odd exponent and an even exponent then it is neither

[@The3nlightened0ne]

@TheGibby13 grade 10!? we'd all be geniuses if he had this since grade school. =D

[@abhinaysingh2756]

f(x)=IxI that is f(x) is defined as absolute (modulus) value of x . this is an example of x raise to one (for matter any odd power of x) but f(x) is always an even function. please comment on that @ khan Academy

[@TheGibby13]

I wish I had this in grade 10 :p

[@thesocialgod]

@Mikej1592 what's the problem with that???

[@rodmur]

Actually, I was wondering, and perhaps to nitpick a bit more. If you look at the Taylor series of an even or odd function, the exponents will be even or odd, I believe. So cos(x) is even because the Taylor series is 1- x^2/2 +x^4/24.... so that might be a way to generalize the definition. Oh, I see now someone (DuckQuickly) already suggested that. Eh, oh well.

[@ermiasmerine5304]

@Gilbert Pankharst so true... I regret not taking accelerated classes in middle school.

[@professorclaustrum8115]

Excellent work explaining what even and odd functions are. I must complement how thorough and simple you made it. I must criticize, however, the lack of any explanation as to WHY it is any good to label a function as being even or odd.

[@bobbysback]

That function has x with the power of 3 in it... THAT'S AN ODD NUMBER!!!

[@Mikej1592]

@thesocialgod he edited it out of the video right after I posted the comment but never responded to my message. However negative 8 plus 1 is not positive 7, should have been negative 7, just in case you were not being sarcastic. :-)

[@nuthalapatiaditya8443]

sir is f(x)=x^2+x+1 an even or odd function?

[@rodmur]

The modulo function... a mod n, I don't believe is either even or odd. There might be examples where it could be made odd (or maybe even), but I don't know of any. Someone more clever than me might figure that out.

[@The3nlightened0ne]

@TheGibby13 we*

[@Mikej1592]

lol that -8+1=7 still bothering me.

[@gobyg-major2057]

There's no such thing as a zero function