function question

[moronatmath]

Hi im new to this board and wanted to know.

Is this function even, odd, or neither?
f(x)=x^2+2x-3

I also wanted to know why if possible. Let me know! Thank you

 

[soroban]

Hello, moronatmath!

Welcome aboard!

Is this function even, odd, or neither? \(\displaystyle \:f(x)\:=\:x^2\,+\,2x\,-\,3\)

There is an "eyeball" method for this . . . examine the exponents on the variable.
\(\displaystyle \;\;\)If all exponents are even, the function is even.
\(\displaystyle \;\;\)If all exponents are odd, the function is odd.
[There is more to the rule, but this works fine for polynomial functions.]

This function has exponents of 2, 1, and 0
\(\displaystyle \;\;\)Note that: \(\displaystyle 3\,=\,3x^0\) . . . an even exponent.

Since some exponents are even and some are odd, this function is a "neither".

 

[moronatmath]

ThANk you very much!!

~themoronatmath