Question

Determine algebraically the whether if thefunction is even, odd, or neither!

Answer 1

Okay, here we have this:

We need to determinate if the function is even, odd, or neither, let's do it:

Considering that a function is even if f(-x)=f(x) for all the real numbers, and that a function is odd if f(-x)=-f(x) for all the real numbers.

Let's find first f(-x) and -f(x):

f(-x)=|-x+2|

-f(x)=-|x+2|

Now let's check if it is even:

f(x)=|x+2|, f(-x)=|-x+2|

Here we can see that f(-x) is diferent of f(x), so the function is not even.

Now let's check if it is odd:

-f(x)=-|x+2|, f(-x)=|-x+2|

Here we can see that -f(x) is diferent of f(-x), so the function is nor odd.

Finally we obtain that the correct answer is neither, it is neither even nor odd.