Graphing Trig + algebra functions

[Miike012]

1. The problem statement, all variables and given/known data

y = 1/x - sin(x)


What is the best strategy to graph this? I am having a difficult time drawing accurate graphs of these types of functions....

[HallsofIvy]

Quite frankly, I think the best way to graph something like that is just to calculate y for a large number of x values and plot those points. Of course, a graphing calculator will do that for you, very rapidly.

However you do it, be sure to distinguish between f(x)= (1/x)- sin(x) and g(x)= 1/(x- sin(x))!

[osnarf]

If you just need a rough graph you can do the following:

First, graph f1(x) = 1/x. Then, graph f2(x) = - sin(x) on the same graph.

Then just add the two together. That's what I usually do.

You'll see what I mean if you graph f1(x) = x^2 and f2(x) = -x^2.

If you add the two together you get a straight line
f(x) = f1(x) + f2(x) = x^2 - x^2 = 0

[Miike012]

Interesting... thank you for the advice... when you say add together you mean add the y-values correct?

[osnarf]

Yeah, exactly. It's the same principle as plotting a bunch of points, it usually just takes less time because you break it into graphs that you already know what they look like.