Draw a graph of periodic extension of a piecewise given function

Question

Let $f(t)$ be a function given as follows: \begin{equation*} f(t)=\begin{cases} 1 \quad &\text{if} \, x \in [0,1) \\ 2 \quad &\text{if} \, x \in [1,2) \\ \end{cases} \end{equation*} Draw the graph of the odd extension of the previous function with period $4$ over the interval $(-4,4)$? How to go ahead with such a function and draw it?

Answer 1

Given the piecewise function, you can graph the function from [0,2) (I assume you've already done that.) Then it tells you that the graph is odd, meaning it is symmetric around the origin. This tells you that f(t)= -1 if x∈[−1,0) and f(t)= -2 if ∈[−2,−1). Now you want to extend the periodic function from (-4,4). It is given that the periodic function has a period of 4. We have already graphed from [-2,2) so you can determine how the graph looks from [2,4) and (-4,2). f(t)= -2 if x∈[2,3), f(t)= -1 if ∈[3,4), f(t)= 2 if x∈[−3,-2), and f(t)= 1 if ∈(−4,-3). Sorry if this is hard to read, I'm also a little unsure about the interval notation I used.