Question

what is y=1/x

Answer 1

A function.

Answer 2

Inverse proportionate

Answer 3

And a hyperbola when graphed.

Answer 4

It is - rectangular hyperbola. It's the first hyperbola most students encounter.

Answer 5

I thought a hyperbola had the normal equation of
\[x^{2} - y{2} = 1\]

Answer 6

A normal hyperbola*

Answer 7

y^2*

Answer 8

Yeah, most are that form, but imagine if you rotate a hyperbola like that? What will it look like?

Answer 9

Holy crap, why do I not know this. Kudos sir. 8)

Answer 10

Haven't worked with hyperbolas alot at all.

Answer 11

Haha well it doesn't really come up except in certain classes... I only remember it from tutoring a kid in a "math analysis" class. I'm not sure it comes up in a regular precalculus class...

Answer 12

INVERSE VARIATION ?

Answer 13

Oh it does, comes under rotation of axes.

General conic equation of a conic is

\[\Large Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\]so if B = 1 and F = -1 you have a y = 1/x

Answer 14

It's probably not included in a lot of precalc classes though, seems more like an optional inclusion.

Answer 15

More interesting, I never seen this before either.

Answer 16

Oh, maybe that's why. They wouldn't teach that in high schools lol.

Answer 17

Some high schools def do - the math analysis kid i tutored was in H.S (but I think that may've been the first/only time i encountered it, and that class covered lots of strange stuff). It's in my class's precalc book, but isn't something i *need* to teach them.

Answer 18

Oh, I see. Thanks for this, it'll be helpful.