Having trouble understanding Odd or even functions of Fourier

[Spoolx]

Homework Statement

Is the function even, odd, or neither

$$y(t) = \frac{2At}{w} for 0<t<\frac{w}{2}$$
$$y(t) = \frac{-2At}{w}+2A for \frac{w}{2}<t<w$$

Homework Equations

even function f(-t) = f(t)
off function f(-t) = -f(t)

The Attempt at a Solution

I just don't understand the concept, any help is appreciated.

 

[SteamKing]

An example of a even function is y = cosine (x) or y = x^2.
An example of an odd function is y = sine (x) or y = x.

If you look a graphs of these functions, what property of their graphs distinguishes an even function from an odd function?

 

[vela]

I believe you meant to specify one piecewise function:
$$y(t) = \begin{cases}
\frac{2At}{w}, & 0 \le t < \frac w2 \\
2A - \frac{2At}{w}, & \frac w2 \le t < w
\end{cases}.$$ This specifies just one period of the function. You want to repeat it so that you have a function defined for all $t$. The question is asking if the resulting function is even, odd, or neither.

 

[Spoolx]

I believe you meant to specify one piecewise function:
$$y(t) = \begin{cases}
\frac{2At}{w}, & 0 \le t < \frac w2 \\
2A - \frac{2At}{w}, & \frac w2 \le t < w
\end{cases}.$$ This specifies just one period of the function. You want to repeat it so that you have a function defined for all $t$. The question is asking if the resulting function is even, odd, or neither.

That is correct, I could not figure out how to do the piecewise function.

I have done a bunch of reading and I still don't get it. If i graph it (see attachment it doesn't appear to be symmetrical about either axis, or maybe I am just missing something)
Thanks

 

[LCKurtz]

That is correct, I could not figure out how to do the piecewise function.

I have done a bunch of reading and I still don't get it. If i graph it (see attachment it doesn't appear to be symmetrical about either axis, or maybe I am just missing something)
Thanks

What you have drawn is just one period. Draw some more of the graph, using the fact that you know what a period looks like, going both directions and see if what you get looks even or odd.

 

[Spoolx]

What you have drawn is just one period. Draw some more of the graph, using the fact that you know what a period looks like, going both directions and see if what you get looks even or odd.

in that case I would say its symmetrical about the y-axis which I believe is like a cos function so even?

 

[LCKurtz]

in that case I would say its symmetrical about the y-axis which I believe is like a cos function so even?

Yes. You can see from the graph that $f(-x)=f(x)$.

 

[Spoolx]

Well I thought I understood it, but I ran into two more problems which don't make sense

To me, they both should be Cos or even functions but the book says the first one is an odd function.

What am I missing?

Thanks so much

 

[benorin]

If u look at the functions, they both have a factor of t, so they are like sin(t) or just t, odd.

 

[LCKurtz]

Well I thought I understood it, but I ran into two more problems which don't make sense

To me, they both should be Cos or even functions but the book says the first one is an odd function.

What am I missing?

Thanks so much

If u look at the functions, they both have a factor of t, so they are like sin(t) or just t, odd.

No benorin, that is not correct at all.

@Spoolx: Generally you should start a new thread with a new question. If you extend those functions by drawing more periods as you did before you will wind up with one of three possibilities: even, odd, or neither. Ignoring the book's answer, tell us what you think and why.