For f(x) = 2x2 +1, the graph is a parabola opening upward with axis of symmetry the y axis. Any two points on the graph of f which are equidistant from the axis of symmetry have opposite x coordinates but have the same y coordinate.
An example is (1, 3) and (-1, 3). Since the horizontal line that goes through these points crosses the graph of f more than once, the graph fails the Horizontal Line Test and consequently f is not one-to-one.
