(a) Note: y is not defined for x = 0, due to division by 0

Hence, x = 0 is not in the domain

(b) Draw up a table of values:

 x -4 -3 -2 -1 1 2 3 4 y 3/4 2/3 1/2 0 2 3/2 4/3 5/4

(c) We know something strange will happen near x = 0 (since the graph is not defined there). So we check what happens at some typical points between x = -1 and x = 1:

when x = −0.5,\ y = 1 + 1/(−0.5) = 1 − 2 = −1

when  x = 0.5,\ y = 1 + 1/(0.5) = 1 + 2 = 3

(d) As the value of x gets closer to 0, the points get closer to the y-axis, although they do not touch it. The y-axis is called an asymptote of the curve.

(To convince yourself of this, plot points where x = 0.4, x = 0.3, x = 0.2, x = 0.1 and even x = 0.01.)

There is another aymptote in this curve: y = 1. Notice the curve does not pass through this value.