Can someone show me how to graph xy = 15?

- anonymous

Can someone show me how to graph xy = 15?

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- e.mccormick

Find y, graph a few points, like the y intercept. and watch out for x=0.

- e.mccormick

Oh, and finding the y intercept is actually a bit of a trick.... you may notice there is not one. There is also not an x intercept.

- e.mccormick

When you solve for y, you get:
\(y=\frac{15}{x}\)
Any x that evenly divides 15 is a good point to use. So \(x=\{-3,-1.5,1.5,3\}\) give useful points.

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- anonymous

Okay.

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- e.mccormick

Then play connect the dots. Remember, you can't cross either the x or y axis.

- e.mccormick

(1,15), (15,1), (-1,-15), (-15,-1) are also there, so you have an idea what happens to the tails.

- e.mccormick

The lack of an x or y intercept is one of the big clues to the shape. Do you know what that means? What quadrants your points are in is the other part of this clue.

- anonymous

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- e.mccormick

Yep! https://www.desmos.com/calculator/n7xd8g8ojy

- anonymous

Thanks!

- anonymous

Could you help me with one more?

- e.mccormick

Sure, but first... one concept from this type graph becomes super important later in math. Can you guess why the graph shoots up and down as it gets close to the origin?

- anonymous

Not exactly sure.

- anonymous

Because it is undefined?

- e.mccormick

\(y=\frac{15}{x}\) Well, what if x is really small? Close to 0.
Say \(x=\frac{1}{100}\)
\[y=\frac{15}{\frac{1}{100}}\\
y=\frac{15}{1}\cdot\frac{100}{1}\\
y=1500\]

- anonymous

Oh, okay.

- e.mccormick

The undefined part then becomes what they call an asymptote. Vertical asymptotes are lines that can not be crossed.

- anonymous

Alright. One more problem?

- e.mccormick

Sure.

- anonymous

Okay.
\[y = \frac{ -18 }{ x }\]

- e.mccormick

Same principal.

- e.mccormick

It just changes what quads because of the -.

- anonymous

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- e.mccormick

The important thing for easy graphing of these are factors of 18. Half points are not bad, but sometimes when you get down to weird numbers it just gets hard to graph nicely.
18 9 6 3 2 1 are all factors of 18. So they make the "easy" points this time. 1.8 is OK, just not as easy to graph as whole numbers and halfs.

- anonymous

Okay.

- e.mccormick

And you will get something like:|dw:1368216529907:dw|Not to scale this time, but I am sure that you get the point by now.

- anonymous

For some reason -1.8,-10 and 1.8,10 aren't plotting right, I know you said it would be a bit harder.

- e.mccormick

(-1.8,10),(1.8,-10)

- anonymous

Yeah, I just realized I did it wrong, thanks.

- e.mccormick

np. Have fun!

- anonymous

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- anonymous

Thanks for the help!

- e.mccormick

Yah, not too terrible once you have the basic concept.

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