The graph must show that the force has both positive and negative x-components, such that the integral of the force between the two times equals zero.
Work Step by Step
According to equation 8.7, the integral of the net force between the 2 times is the impulse of the force. The x-component of the momentum is unchanged between those 2 times, so the x-component of the impulse (change in momentum) is zero. If the integral of a function is zero, but the function itself is not zero for the entire time, then the function must take on both positive and negative values (because the signed area between the graph and the t-axis is zero).