Answer
See the image below for the graph.
The function is one-to-one function.
Work Step by Step
$f(x)=x\times|x|$, we can sketch the graph for the following function using a graphing calculator (See the image above).
As we can clearly see from the graph it is a one-to-one function, since there is no $y$ value of the graph which corresponds to more than one $x$ value.
