how to graph : 0<x<1,z<x<1,0<y<x

Question

please tell me how to generally graph inequalities in 3D

Answer 1

It is done in the same way as graphing inequalities in 2D, but is difficult or impossible to do on 2D paper.

Typically a computer generated 3D graph needs to be used.

You would sketch certain lines to form the boundaries of the inequalities:

For 0<x<1, you need to sketch lines x=0 and x=1

For z<x<1, you need to sketch the line x=z

For 0<y<x, you need to sketch lines y=0 and y=x

Then you shade in the volume of space in 3D that meets the criteria of the inequalities (x must be greater than z for example, so don't shade any points where z is greater than x). I don't think this can be done on 2D paper, you would need a computer with 3D graphing ability.

The 3 inequalities you have will basically form a triangle near the origin on the 3D graph.

Hope this helps! :)