How do you read this graph:
Function is: $f(x, z) = 1-e^{xz}$
How would I read the graph say $x = 3, z = 0.8$, which would make $y = 0.9092820647$
How do I find $y$ on the graph?
Thanks.
[Math] Reading a 3D graph
functionsgeometrygraphing-functions
Related Solutions
Two possible guesses.
Probability Density: $\large y=ce^{-\left(\frac{x-k}{h}\right)^2}$
I don't know what a name for this is, but another similar graph is $\displaystyle y=\frac{c}{1+(h(x-k))^2}$.
First off, I agree that the correct approach is to conflate the two variables $s$ and $p$ into one variable, say, $m=s\times p$. This effectively allows you to reduce the problem by one dimension. Thus the problem becomes how to visualize the equation $$m\times r = c\times(1+i-r).$$ I emphasize the generic term visualize rather then the more precise term $graph$ because, as mentioned, the graph lives in 4D space - one dimension for each variable. There are other ways to visualize an equation, though. One common technique to visualize an equation involving three variables is to plot the surface consisting of all points where the equation is true. If $c=0$ in the above equation, for example, we get the equation $m\times r=0$, which is true when either $m=0$ or $r=0$. The graph in the $(m,r)$-plane consists of just the $m$ and $r$ axes together. When extended into $(m,r,i)$ space, this consists of all points of the form $(0,r,i)$ or $(m,0,i)$, which looks like so:
To visualize your equation involving four variables, we sketch several representative contour plots from the family of equations for various choices of $c$. We might place them all together in one plot:
or in several:
Finally, if you find yourself facing a genuine function of five variables with no easy way to conflate two of them, you could always sketch a 2D grid of 3D contours (rather than the 1D grid above). Similarly, this function of four variables could be visualized as a 2D grid of 2D contours:
Best Answer
I think that the easiest thing for you to do would be to find the location of $x$ and $z$ first. Just like you would on a two dimensional graph. Then since $y$ is your height, just visually raise the point until it hits the curves of your graph. That's where the point is.