For instance, this morning in class.
We are working with inverse relations with my kids; trying to show that every mapping has an inverse mapping, but that doesn't mean either one of them is a function... and I showed them a complicated implicit function. I started withx^2 + 3xy + 2xy^2 = 7 just picked something off the top of my head...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhj_x40rUh87dwgDnUS2e7zEF-jgio0E3AQ_k1uoRyYtcOb5uXQxie8EgWJQ5M7IFXXv9D3lUDX25ZMaD9RWBqwt-nXJffCom-A26ggz8ho87kJZpEXiAxR06P0vI5vqH_OfOpqbkglBf4/s320/woops1.jpg)
It was interesting, then we talked about what it would look like if we flipped it around by interchanging the x's and y's.
y^2+3yx+2yx^2=7 but???
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAPCdHryRmtWHhCS3lZ0zKtLCjepLmDdHEojx9S8xCoNygvpIbbMajxf1GDHvTvYuhg1lyzBhbAAlPsF2OQz1rtzsQyL5ekjcENNXzepqyKdLq9tzHdmKwEkYdz8sajd1wyX5CSnTbmbI/s320/woops2.jpg)
I couldn't imagine what was amiss, but retyped it as y^2 + 3xy + 3x^2 y=7
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN1ZOeMW3lfJppwF03QUU0daxl6f47FGWys9ta95eINdNGuu5WNvLO3gmRiGIfBpbK9-0QD_uA7o1RIDShEUA63D1zoij2fPzmnLVqxp0Re4kZH4lH9ztrca_LmoUCBGyXG3Ujir04sNw/s320/woops3.jpg)
Curious, I experimented...was it the order yx verses xy that confused it? tried a rectangular hyperbola
xy=1 no problem.... yx=1 this does not compute???
Ok, so what happens if I type in x=y^2... I get the typical parabola orientation you would expect with y=x^2, centered at the origin and opening up along the y? axis. Neither axis was labeled in this image, but the graph is labeled "y from -1 to 1"
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdC81CJqjsnNLWYND9GIkVDPYIYbr_S6aDEHxbJ6ZwYeTikTLkSIEHPmP03TmMYlzcRxQdchqXMFJNmEKqn8bRG970_EkJCZUEpSNuHwE4QZ_TONQn6A2tkP0A3MlF5KS86zS2_bmv76s/s320/woops5.jpg)
y^2 = x shows the right opening parabola you would expect, with both axes labeled.
One of the many idiosyncrasies of Wolfram alpha.
2 comments:
Mathematica assumes that if you type a multi-letter string like "height" that you mean a single variable.
Same with xy and yx - a common error in Mathematica users is to type those things and forget that Mathematica thinks those are new variables rather than products.
Alpha apparently has a script that detects xy and inserts the * sign, but not the same for yx.
So, type the * signs explicitly and you'll be fine.
y^2+3y*x+2y*x^2=7 gives you the plot you want.
Josh, Maybe that's true, but if I write a z in place of the (yx) in each place, then I have an ellipse... and if I enter that into W_alpha, I get an ellipse, the x and y seem to be no favorites.. in fact, I just tried t^2 + r^2 = 1 and it gave me a graph of a circle... so again, I wonder why it didn't graph "something" even if it thought it was another variable.
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