Question

Let $f$ be the function on [0,1] given by $f\left(x\right)=x\sin \frac{1}{x}$ for $x\ne 0$ and $f\left(0\right)=0$. Then f is

• A. discontinuous but bounded
• B. differentiable
• C. continuous but not bounded
• D. continuous and bounded

Answer 1

The correct option is D continuous and bounded

So from the graph we can say that the function is continuous as well as bounded(between lines $y=x$ and $y=-x$).