#1**+13 **

if f(x) = f(-x), then the function is even. So, f(-x) = 2^-x which does not equal 2^x.

However, if f(-x) = -f(x), then the function is odd. So -f(x) = -2^x which does not equal f(-x) = 2^-x.

**f(x) = 2^x is neither even nor odd.**

AzizHusain
Jul 29, 2014

#1**+13 **

Best Answer

if f(x) = f(-x), then the function is even. So, f(-x) = 2^-x which does not equal 2^x.

However, if f(-x) = -f(x), then the function is odd. So -f(x) = -2^x which does not equal f(-x) = 2^-x.

**f(x) = 2^x is neither even nor odd.**

AzizHusain
Jul 29, 2014

#2**+10 **

Also,

A function that is **even** has the y axis (x=0) as an axis of symmetry f(x)=f(-x)

A function that is **odd** has point symmetry about the origin. This means that if it is rotated 180 degrees it will be the same. f(-x)=-f(x)

This is what 2^{x} looks like. You can see that it is not symmetrical about the y axis.

And it does not have point symmetry about (0,0)

so it is not an even function or an odd function.

Melody
Jul 30, 2014

#3**+5 **

Let me add one thing to what Melody is saying......we can always "test" whether a function is even by replacing x with -x.....if the reults are the same, then the function is even.

Then, is 2^{(x)} = 2^{(-x)} ???........NO !!!

Note that a function like x^{2} **is** even, because...

x^{2} = (-x)^{2}

And this is exactly what Melody said......

CPhill
Jul 30, 2014

#4**0 **

Thanks Chris,

Aziz had already done that but perhaps your working is a bit clearer.

Melody
Jul 30, 2014