The rational function might have the aymptote and holes. In the most left picture, there are good example of the aymptote. According to the value of rates of change, the slope of this rational function is always negative, but there are two asymptotes, so the function value doesnot keep dcreasing on the graph. Also, the rates of change is decreasing slower than other place near 0. However, after passing through 0, the speed of this function gets quite fast to go to the post-office. The both sides of the center of the line gets steeper and steepe. Furthermore, the horizontal asymptotes is y=0, so the left function gets faste and fasterfrom y=0. Also, the right line gets slower and slower to 0. 

     The rate of changes is not equal to 0 any points, the line of the function is curved. Therefore, the right side  line gets flatter and then the shape of the funtion is like decaying function. It is decaying from the positive inflinity. the fnction in the center comes from the positive to negative infini, but the rate of change is smaller. Therefore, the line of the function is made flatter once, and then steeper again. Firnally, line in the left side gets steeper to negative infinity since the rate of change getsmore and more smaller.