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Question 214802: I would like to know how to graph in 3 dimensions. I can never visualize it. Would you please do an example?
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Best source I could find online is at the following web address:
http://graph.seriesmathstudy.com/
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just copy that url into your browser address bar and hit the return.
that will take you to the website where the graph tool is located.
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the graph will show up as 2 dimensional.
that is the default.
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the box on the upper right will say f(x) =
you enter your equation in the box.
say you enter x in the box.
then click on graph it.
you will see a 2 dimensional graph for the line y = x.
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select 3D
then enter your equation again (the tool defaults to x*xin(x) every time you set somethint to another value so you keep having to reenter your equation or at least check to see if your equation is still in the equation box).
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once you select 3D, the title on the equation box will read f(x,y) = rather than f(x) =
enter x again in the equation box and then slick on graph it.
you will see a 3 dimensional graph of z = x (not y = x)
this is because f(x) is graphed as y = f(x), and f(x,y) is graphed as z = f(x,y)
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uncheck motion to stop the graph from spinning automonously.
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you can orient the graph any way you want by clicking anywhere in the graph and dragging your mouse in different directions while holding the left mouse button down.
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if you orient the graph so the z axis is vertical and the x access is hoizontal and the y axis points directly towards you then you will see that the graph looks like the 2 dimensional graph of y = x except this graph is showing z = x.
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in 2 dimensions, y = x is a line.
in 3 dimensions, z = x is a plane.
it has depth as well.
this is because y value is undefined meaning it can be any value so the graph is a plane showing z = x and y can be any value.
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you can play with this graph to visualize what's happening.
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try y = x^2 in 2 dimensions and then try z = x^2 in 3 dimensions. you'll see that y = x^2 is a parabola in 2 dimensions and is a parabolic plane in 3 dimensions. it has depth as well.
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check it out.
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