/sci/ - Science & Math » Thread #7616754

[5 / 1 / ?]

145KiB, 560x598, y.png

Anonymous Mon 26 Oct 2015 12:00:38 No.7616754 View Reply Report Delete

Quoted By: >>7616770 >>7616793 >>7616857

People of /sci/, I am naturally a simple minded /b/ian. However, the other night before going to sleep, I pondered a particular scenario;
'What would the graph of *y = y/x* look like?'
I was much to tired to actually look it up last night, so I theorized it was just impossible. I mean how could a function have an answer that is the function divided by the variable? Wouldn't said variable need to create the function first?
So it was when I awoke today that I mimicked every other great scholar, and hit the highway to Googletown. I was shocked when this 3-dimensional graph was presented to me.
So to wrap this short story up, is there anyone who can explain this graph to me?
Why did the z-axis become relevant and what does it portray?
Is the colored section the answers satisfied or the asymptotes of the equation?
Please help.

Anonymous

Anonymous Mon 26 Oct 2015 12:07:13 No.7616770 Report Delete

Quoted By:

>>7616754
Simplfy
y = y/x
1 = 1/x
x = 1

It's a straight line.

Anonymous

Anonymous Mon 26 Oct 2015 12:14:59 No.7616793 Report Delete

Quoted By:

>>7616754
y=y/x is a straight line, your graph is f(x) =y/x which has two variables that modify the f(x) which is z hence the 3D

Anonymous

Anonymous Mon 26 Oct 2015 12:54:51 No.7616857 Report Delete

Quoted By: >>7616870

>>7616754

Expressions and equations given in terms of coordinate geometry are not necessarily functions, OP. For example, the equation x^2 + y^2 = 1 describes a circle with a radius of 1, which is centered on the point (0,0).

For example, "x = 1", assuming we're setting things up in the usual sense that these letters are frequently used ( y = f(x) , say --- or not!), well, it turns out that this is not a function at all, but rather, its graph in R^2 is just a vertical line one unit to the right of the y-axis. Or in R^3, it's the plane just to the right.

Such equations as the above can be interpreted like so: "Okay, say you're in a plane, a space, etc. Find all the points which satisfy such-and-such expressions." Thus you can describe regions via inequalities, verbalized rules, wibbly-wobbly-circle-travellers, etc.

So, in a plane (or space, for that matter, but let's stick with plane), your original expression y = y / x can be interpreted as a prompt: "Find all the points such that the second coordinate equals the second divided by the first".

Whenever you're doing division, you need to be mindful of any spots where you might divide by zero, which for our purposes, is RIGHT OUT. In particular, you should immediately be leery of any situation where either x or y is zero (the axes), just based on your original expression. But this ends up being moot since x = 1 like that guy said; a completist could remark that there is a point discontinuity when the above line crosses the x-axis (where x is zero and thus Ya Can't Do That).

You seem to be using some function plotter which is interpreting your thing as two variables (which produces a 3D plot), like the other guy said (instead of my find-all-the-points interpreteation).

Anonymous

Anonymous Mon 26 Oct 2015 13:01:07 No.7616870 Report Delete

Quoted By:

>>7616857

ugh, never mind the point discontinuity nonsense, brain fart.

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