Well, let's see. Y cannot be negative, and cannot be zero, though it approaches zero as x becomes more negative. As x increases, y increases. The line crosses the y axis at y=1, x=0; the line never crosses the x axis.
So it sounds a lot like an exponential function. In fact, couldn't you say it's a different form of an exponential function? Rewrite it as y = exp[ a*x].
You can't spell "justice" without ISTJ.
Well, yeah, it's exponential function, actually. I don't recognize form y = exp[ a*x]. I know it only as y = a^x (there is no fuckin' upper index so I must write it as ^x)
Actually, you were almost right. But Y will not approach zero as x become more negative, and Y won't increase as X increase.. think about it
The sad thing is that they don't teach this stuff in school--then they expect you to know it in university.
In school before university, we covered graph behaviors (you know, as general concepts) less times than I count on my fingers. A passing reference. You only really learn it from being forced to use it.
That's why I still can't look at a problem like Gauche's example and just "know" what shape the graph will take. You saw I had to analyze it.
Edit: Oh shoot, you're right. It decreases from left to right, approaching zero as it x increases, because (1/2) is less than one. When the power is a fraction, it flips the behavior. To make it fit the usual form we can rewrite it as y = 2^(-x) , because 2 = (1/2)^(-1). There, that looks better.
Another way to write an exponential is just y = e^(a*x)
Last edited by Cimarron; 12-16-2008 at 01:21 PM. Reason: analyzing
You can't spell "justice" without ISTJ.
Teaching methods can tend to suck. My math teacher assigned stuff from the book everyday, but rarely went through the book's introductions for each section. She just took problems from the practice part, and taught us the concepts with that. When I tried going back through the book's explanations of things to learn how to do stuff, I got slapped on the wrist for doing things "the wrong way." It just bothered me because I didn't like taking notes. I'd rather watch her do the problems then go through the book later if I need to.
You know, I'm still in High School (..I'm 19 this week, and I'm in 4th - finishing year) and I'm going to make "finishing exams" from maths (and physics and my native language/literaure and english). We were learning that crap in the first 3 years. Now we are revising that old stuff and learning new things - advanced derivations and integrals
This is amusing, because that's not how I would go about solve that problem at all.
I would first look at it and recognize that it's an exponential function (e^x and 0.5^x are just both numbers to the power of x). Then I would go about finding its derivative y=ln(1/2)*(1/2)^x. Since the derivative is always negative, it will always be decreasing.
You seem to go around the intuitive jumps to get to a similar place.