Make the given changes in the indicated examples of this section and then plot the graphs.

In Example 4, change the x in the denominator to x − 1.

Data from Example 4

Graph the function

In finding the points on this graph, as shown in Fig. 3.18, note that y is not defined for x = 0, due to division by zero. Thus, x = 0 is not in the domain, and no point on the graph will have an x-coordinate of zero. This means the curve will not cross the y-axis. Although we cannot let x = 0, we can choose other values for x between −1 and 1 that are close to zero. In doing so, we find that as x gets closer to zero, the points get closer to the y-axis, although they do not reach or touch it. In this case, the y-axis is called an asymptote of the curve.

Fig. 3.18.

y = 1 + 1 X