Graphing Parametric Equations: Solving for t^2, t^4, and t^6

[nameVoid]

t^2,t^4,t^6

Trying to graph this

I have the traces
x=y^2 for x>=0 in xy
Also x=z^3 for z>=0 in xz
And z=y^(3/2) for y>=0 in yz

Parametricplot3d in mathematics does nothing to get a picture for this graph and drawing is proofing difficult
In general what is the best way to plot these when it's not obvious plug in for t?

 

[SteamKing]

It's not clear what you are trying to do.

Is your function f(x,y,z) = (t^2, t^4, t^6) perhaps? Or something else?

 

[nameVoid]

Yes that is the function of x y z
I am trying to graph it

 

[haruspex]

It's not clear what you are trying to do.

Is your function f(x,y,z) = (t^2, t^4, t^6) perhaps? Or something else?

I think you mean, vectorially, r(t) = (t^2, t^4, t^6), i.e. x = t^2 etc..
But from the OP,

x=y^2 for x>=0 in xy
Also x=z^3 for z>=0 in xz

suggests r(t) = (t^6, t^4, t^2).

what is the best way to plot these when it's not obvious plug in for t?

It depends what range of t you want to sketch it for.
It's kind of hard to sketch 3D curves. What exactly have you been asked to do?

 

[nameVoid]

Sketch the curve
mathematica doesn't help

 

[nameVoid]

The book asks for a sketch I assume there is a reasonable way
Plot t values?

 

[Bill Simpson]

Is this what you are looking for?

ParametricPlot3D[{t^2, t^4, t^6}, {t, 0, 1}]

If it isn't then perhaps you can explain what is incorrect about that.

 

[nameVoid]

Is gives a line I am under the impression that the graph is a surface
What's throwing me off is the book taking the trace in each plane
Sint,cost,t cylinder along z

 

[Ray Vickson]

Is gives a line I am under the impression that the graph is a surface
What's throwing me off is the book taking the trace in each plane
Sint,cost,t cylinder along z

No: the point-set you describe is a one-dimensional object = a curve in 3d. If you wanted a surface you would need two independent variables, so you would need to have something like three functions x(u,v), y(u,v), z(u,v) in two variables u and v.

 

[nameVoid]

In cost,sint,t
z for all real isn't a cylinder?

 

[Bill Simpson]

In cost,sint,t z for all real isn't a cylinder?

Nope.

ParametricPlot3D[{Cos[t], Sin[t], t}, {t, 0, 4 Pi}]

It is perhaps difficult to get a really good 3D view of it, but try from different angles and guess what it is.