What's the graph for this periodic function

Question

Please show the graph for $-2\pi <t<4\pi$ $$f(t)=e^{-t}$$ $$f(t)=f(t\pm2\pi)$$

Is there an online plotter for periodic functions?

Answer 1

You can look at it this way: At first $f(t)$ is only defined for $-2\pi<t\leq2\pi$. This would just be the normal graph of $f(t)$, exept you only draw the part within the given interval. If you want to know the value of $f(t)$ for a $t$ outside this interval, you use the fact that $f(t)=f(t\pm2\pi)$, so you can go back with steps of $2\pi$ untill you are back in the original interval. This is how you get to know the values of $f(t)$ on all of $\mathbb R$.

As for the graph, it will be that little piece of $e^{-t}$ on $(-2\pi,2\pi]$. Only there will be a great number of these segments and they're all at a fixed distance of their direct predecessor.