How do you graph the function y=−2x?

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)=−2x, you start from the function g(x)=1x and make two changes: you put a minus sign at the beginning, and you multiply by 2:

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

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 −2x (assuming you're familiar with the one of 1x)

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