sorry about this

October 23, 2006 5:43 AM

what is a (left-to-right) mirror image of the standard logarithmic graph called?

mirror image is a pretty poor description, but, on the x/y axis, going to the right and down. something, say, starting at (0,10), passing through (10,7) and heading down into the negative y axis as it progresses into the positive x. is there a name for this?

posted by hayeled to science & nature (16 comments total)

Exponential graph? y=10^x should do it.

I believe the phrase you were looking for wasn't "mirror" but rather "inverse function". log base ten and 10^x actually *are* mirror images of each other, but the mirror is the line x=y.

On re-read, I"m not quite sure what you're looking for, but what I've already written may help nonetheless.
posted by notsnot at 5:55 AM on October 23, 2006

y = 10^x will not fit (0, 10) and (10, 7).

Can you give us an equation for the curve you want to name? I'm fairly confused by this description.
posted by grouse at 6:00 AM on October 23, 2006

Yeah, I caught that on re-read.
posted by notsnot at 6:05 AM on October 23, 2006

Like this one? The form you want, with the slope getting more extreme as you go to the right, is an exponential graph. From the points you listed, it sounds like you want it to go negative. Since a pure y = -c^x graph would be in negative territory everywhere, we have to add a constant. I chose constants to get the data points you asked about (though other choices would work too).
posted by raf at 6:09 AM on October 23, 2006

Here's another graph that fits the points you listed.

Basically any graph of the form y = 10 + (3/c^10) - (3/c^10)c^x will work, with varying degrees of sharpness.
posted by raf at 6:13 AM on October 23, 2006

y = log10(x) gives you a graph with a line sloping upwards, I think he means the other way around, so that it starts really high, and slopes down as x increases. Like all those "long tail" graphs that are oh-so-trendy.

No idea on the technical term though.
posted by public at 6:14 AM on October 23, 2006

He's talking about a graph of a function like

f(x) = c-a**x

where c and a are constants

in the above example

c=10
a=log(3)

It's just an upside down exponential curve

If you express it as

f(x) = c+a**x

then a becomes a complex constant

in the above example

a = log(-3) = approx 0.477121255 + 1.36437635 i

so you could say it's a complex exponential graph I guess.

(disclaimer: it's twenty years since I took math)
posted by unSane at 6:16 AM on October 23, 2006

Actually, I have an error in my equation that affects things for small c. But it's close.
posted by raf at 6:16 AM on October 23, 2006

yeah, sorry about that guys, the naming of exact points may have been misleading.
specifically speaking, i'm trying to describe a process, where the efficiency of the process decreases with time, even though the inputs remain the same. i have to write this in a descriptive manner for the layman.
so, if you plot a graph where the efficiency gradually decreases and then drops off significantly, how would you describe this curve.
it's not logarithmic, it's...

i'm just after a general term. not logarithmic, not exponential, not inverse logarithmic, um...
posted by hayeled at 6:34 AM on October 23, 2006

how would you describe this curve

I would describe it as "the efficiency gradually decreases and then drops off significantly". That's perfectly cogent.

You shouldn't use 'logarithmic' or 'exponential' or whatever unless your simulation exactly fits that mathematical function -- they are precise descriptions of a particular kind of relationship, not just vague descriptions of a general shape.
posted by chrismear at 6:40 AM on October 23, 2006

You think the layman knows what a logarithmic curve looks like? Come on. Anyway, I would describe it as a "negative exponential curve" (920 Google hits).
posted by grouse at 6:42 AM on October 23, 2006

On posting, much better to listen to chrismear.
posted by grouse at 6:43 AM on October 23, 2006

If you want to write it in a descriptive manner for the layman then just describe the efficiency as dropping off a cliff at some point. There's no simple function that does what you want that I can think of, at least not one that the layman will know.

Since your efficiency shouldn't hit zero probably, and certainly shouldn't go negative you'd want one of the sigmoid functions suitably scaled, flipped and all that.
posted by edd at 6:44 AM on October 23, 2006

actually, i think raf was correct and i should have known this. this should be a lesson to us all to never write reports after wine.
and there's a measure of wisdom in the words of chris too.

but to bypass that, raf, if you're still out there, would you describe this as "negative exponential"?

oh, damn, preview.

right. layman means mine managers. there's a fine line of being clever but not too clever that you have to tread. my only hassle with the term negative exponential is -(x^y) vs (-x^y), but it's a term i think i'll play with.

thanks all for taking the time.
posted by hayeled at 7:16 AM on October 23, 2006

If it's any help, a graph which starts a long way from the Y axis and approaches more and more closely to the Y axis without actually touching it as X increases (eg Y = 1/X) is called asymptotic to the Y axis.
posted by unSane at 8:17 AM on October 23, 2006

Yea, I would call this a negative exponential.
posted by raf at 4:26 PM on October 23, 2006