The correct answer is B. It fails the vertical line test.
Step-by-step explanation:
The given function is a quadratic function of the form f(x) = 2x²-3x+1.
To determine if this function is a one-to-one function, we can use the horizontal line test. If any horizontal line intersects the graph of a function at more than one point, then the function is not one-to-one.
However, if we draw a horizontal line through the graph of the function, we can see that it intersects the function at multiple points. Therefore, the given function is not a one-to-one function.
The vertical line test is used to determine whether a relation is a function or not. If any vertical line intersects the graph of the relation more than once, then the relation is not a function.
If we draw any vertical line through the graph of the function, it intersects the graph at most two points, which means the function passes the vertical line test. Therefore, the given function is a function.
However, since there exists a vertical line that intersects the graph of the function more than once, we can conclude that the function fails the vertical line test.
Therefore, the correct answer is B. It fails the vertical line test.