(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`.)

Graph of `y=1+1/x`, a hyperbola. It's a discontinuous function.

There is another asymptote in this curve: `y = 1`, which is marked with a dashed line. Notice the curve does not pass through this value.

Please support IntMath!