Question

How do you graph the function `y = -2/x`?

Answer 1

graph{-2/x [-10, 10, -5, 5]}

Explanation:

Of course you can only have an idea of how the graph goes: if you need it to be drawn perfectly, you can only use some graphing tool.

Anyway, you can see that, to obtain `f(x)=-2/x`, you start from the function `g(x)=1/x` and make two changes: you put a minus sign at the beginning, and you multiply by `2`:

`1/x` (change the sign)---> `-1/x` (multiply by two) ---> `-2/x`.

So, all we need to do is knowing how these manipulations affect the graph of a function.
If you know the graph of the function `f(x)`, then the graph of the function `-f(x)` is simply the graph of `f(x)` upside down, or to better say, reflected with respect to the `x`-axis.

On the other hand, a numerical multiplication simply stretches (or compresses) the graph, so it doesn't affect it's shape very much.

This considerations should make it possible to you to figure the graph of `-2/x` (assuming you're familiar with the one of `1/x`)