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http://www.geogebra.org Download geogebra and type "f(x) = 3^x -2 " in the input bar at the bottom. :)
In all seriousness, geogebra is a FANTASTIC (and free, and powerful) program for dynamically visualizing graphs.
Well thanks. I'm glad it wasn't a whole gigabyte or something. I already downloaded it.
I made a quick video about how to use the most basic features. I can link it if you're interested. Geogebra is GREAT for exploring what happens to a graph if you change a , b, c, d in a function like: y = ax^3 + bx^2 + cx + d etc
use wolfram, man plot 3^x -2 http://www.wolframalpha.com/
Though I must say.I'm not sure how it got THAT from what I put in.
Yes I'm aware of wolfram and google and all these other fancy websites. I need to know the logic behind it though.
@wedontneednoedukation -- do you know how to plot, say y = x^2 by hand? The idea that you input a value of x (say, 3) , then square it (3)^2 =9 and that result is your value of y? So you then plot (3,9). Then pick another value of x , say 2 then square that... get 4 .. and plot (2,4) etc.?
I can't plot any function, formula, or equation or anything by hand at all.
Ahh, ok. So let's take a step back for a second: 1) Do you know how to plot *point* on the plane? Like, can you plot (-3, 2), (3,2) and (0,5), and (-5,0) with ease? 2) Do you understand the concept of "x is the input" and "a function takes you input, does something to it (adds, subtracts, raises to powers, multiplies, divides, etc.) and then gives an output" and "y is the output"? Cuz before you start graphing, those are two super duper important ideas to have going in.
1. Yes 2. Yes.
Ah, k. That's a very good start then. So with plotting functions, first recognize that there are several very basic kinds of functions: 1) polynomials -- powers of x added together f = x f = 3x^2 - 4x +1 f = -x^2 + 3 etc. are all polynomials. 2) trig functions y = sin(x) y = cos(x) y = tan(x) (which is just sin(x) divided by cos(x) ) 3) exponential and log functions h = ln(x) h = e^x etc
Playing around with this GeoGebra tool I can sort of see the relationship. 1^x is a straight line across 2^x it curves upward 3^x it curves upward even steeper.
Oh and it starts it 1. So if it's minus 2 it will curve upward from -1.