We see that the points of the graph of the function never attain a y-value of 0. Thus f is never equal to 0 for real numbers, hence we can disqualify all the necessary answers already (only answer not against this is 2). Nevertheless, we can show that this is the right answer. The graph is called a parabola, so it is represents a second order polynomial. These polynomials have either 2 real or 2 complex solutions. Since this does not have real solutions (at the lowest point of that polynomial the y-value is 4) the correct answer is b).
