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## Homework Statement

Hello everyone,

I'm new to the great field that is Fourier analysis, and have a question about the way in which to determine if the function is a odd or even function.

Given the function, of one period

f(x) = { x; 0 <= x < =1, 1; 1 < x < 2, (3 -x); 2 <= x <= 3:

Is there a definitive way in which you can determine if this function will be even about the y axis or odd about the x axis.

## Homework Equations

f(-x) = f(x) (even)

f(-x) = -f(x) (odd)

## The Attempt at a Solution

Drawing this function I immediately thought that it was even, although on second thought the function could indeed go down into the 3rd quadrant in the Cartesian coordinate system when repeated in the negative x direction. So I turned to numerical analysis.

Is it correct to use the relevant equations as follows?

f(-x) = { -x; 0>= -x>=-1, 1; -1>=-x>=-2, (3 + x); -2>=-x>=-3.

As you would then have a negative slope going from -1 to 0, the constant remains the same in the negative x direction and a positive slope in the -3 to -2 boundaries.

Wouldn't this imply that it is an even function? Or, the only way to really know is if the function boundary conditions that are initially given, includes the area in the negative x direction?