When x=0,y=1−1=0, so we can rule out (d) and (e). To work out the number of x-axis intersection points, consider (x−1)2=cos(πx). The shape of these graphs means they cannot intersect 6 times (eliminating (b)). The answer cannot be (c), because we know there is a crossing point x=2, but that y is positive when x=1. So the answer is (a).