I'm have a surface z=e^(y-x^2)

And I'm told to sketch the three level curves at z=1,4,16. I can't recognise what shape the surface is. I tried re-arranging but the variables being of different degrees is confusing me especially given the values of z. I thought it would be a sphere or something. Could I get some help?

Question

I'm have a surface z=e^(y-x^2)

And I'm told to sketch the three level curves at z=1,4,16. I can't recognise what shape the surface is. I tried re-arranging but the variables being of different degrees is confusing me especially given the values of z. I thought it would be a sphere or something. Could I get some help?

precal · Answer

Try plotting it using winplot.  Winplot is a free program.  It appears to be 3D.

anonymous · Answer

Thanks but I'll need to know how to do the question without the use of any software.

precal · Answer

Yes, but it should give you an idea of what you are working with.  It is ok to use technology to work backwards.  Winplot is a great program once you learn to use it.