Expert: Bobby Soltani - 4/18/2005

Question
Hi-
I have a homework assignment do tonight and I am a little confused about the function f(x)=3.
Is it even or neither even nor odd. I understand how to solve even and odd functions but this "simple" one confuses me b/c there is no value of x to solve for.

thanks of your help!

Answer
Hi Sherry,

These "simple" functions can be the most confusing.  However, you should apply the same test as other functions that involve x.  Here's how:

If f(x) = f(-x), the function is even.

f(x) = 3
and
f(-x) = 3
when we plug -x in for x, the function is still 3 because there are no x's to substitute for.

so, f(x) = f(-x).  It is an even function.

For completeness, let's test for oddness.

If f(-x) = -f(x), the function is odd.
f(x) = 3
-f(x) = -3
So, they are not equal and the function is not odd.

Another way to tell is if the graph is symetric about the y-axis, it is an even function.  If it is symetric about the origin.

Let me know if you have any questions.

Bobby