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

1 Answer
KillerBunny
Sep 3, 2015

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#)

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