# How do you graph y =7/x?

Jul 22, 2015

Your function will give you a two part curve looking like the wings of a butterfly!

#### Explanation:

You first need to determine the $x$ values that cannot be accepted by your function. In this case you do not want a division by zero so you need that:
$x \ne 0$
The $y$ axis will then become a VERTICAL asymptote of your function; the graph of your function will get near and near to the $y$ axis without ever crossing it.

If you try to get near (but not equal) to zero; you'll see that your function becomes very big (positively or negatively). You express this idea by using the concept of LIMIT:
${\lim}_{x \to {0}^{+}} \frac{7}{x} = + \infty$
${\lim}_{x \to {0}^{-}} \frac{7}{x} = - \infty$
This means that when you approximate zero from the right (${0}^{+}$) or the left (${0}^{-}$) the function becomes big (positively or negatively).

On the other hand when $x$ becomes very big the function tends to zero (gets very small!!!).
${\lim}_{x \to \infty} \frac{7}{x} = 0$

So, basically, your graph will look like the wings of a butterfly!!!
graph{7/x [-10, 10, -5, 5]}