Answer
For the graph see the image below.
This function is not a one-to-one function.
Work Step by Step
$f(x)=\sqrt{x^3-4x+1}$, 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 not a one-to-one function, since there is a $y$ value of the graph which corresponds to more than one $x$ value.