Let $f(x)$ be a periodic function in $x$ with period 2, and $f(x) =|x|−x$ for $−1< x≤1$. Sketch the graph of the curve $y=f(x)$ in the interval $[−3,3]$.
$f(x) =|x|−x$ seems not to be a periodic function, though, so how can I solve the question? Thank you!
Expanding David's comment, taking it step by step, first we have the function $f$ that's stated to be periodic with period 2, but we don't know what it looks like. Then, it's defined to be $f(x) =|x|−x$ for just the interval $(-1, 1]$.
Note that it's only for that specific interval that the function equals $|x|−x$. That can be evaluated to be this;
We've got what the function is for an interval of 2 units now*. We can use that as a repeating unit and make the rest of the graph.
Also note that the endpoints aren't both included in the graph, so you'll have to pay attention while completing it.
*Well, sort of. The leftmost point isn't in that '2 units'. But it'll work out when you think it through for the rest of the graph.