# Reading a 3D graph

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.

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Are you just having trouble visualizing $y$? – MITjanitor Feb 18 '13 at 4:30
Yeah I guess so, like how do I find the point (3, 0.75, 0.6) (x, y, z) on the graph? – Cypras Feb 18 '13 at 4:31

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.

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It is much harder on a 3d graph to read points off. Partly that is because the axes are not orthogonal, and partly that is because each point on the graph as represented in 2d could be any of the points on a line in 3d. So my answer to the question is "Sorry, you can't."

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Would have been nice if my tutor had said that you can't read the points and I wouldn't have tried for ages to figure it out. Thanks. – Cypras Feb 18 '13 at 4:37

Your gridlines presumably represent the X and Z coordinates on the grid. So basically, your point (3,y,0.8) is an intersection of gridlines I pointed with green circle. To prove graphically that y~=0.91, draw a line I shown in cyan with N on it, it is equal and parallel to a box side fraction with another N on it. And then you just draw a line parallel to another box side to your measures.

Looks ~0.9 to me, but I drew it very fast, just to show the idea

The graph

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