(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`.)

12345-1-2-3-4-512345-1-2-3-4xy

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

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

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