Draw a contour map of the function showing several level curves.

[jheld]

Homework Statement

Draw a contour map of the function showing several level curves.

f(x,y) = x^3 - y

Homework Equations

f(x, y) = x^3 - y

The Attempt at a Solution

I think I should be finding the domain and range, but other than that I am not sure what else I need to do.

 

[HallsofIvy]

Homework Statement

Draw a contour map of the function showing several level curves.

f(x,y) = x^3 - y

Homework Equations

f(x, y) = x^3 - y

The Attempt at a Solution

I think I should be finding the domain and range, but other than that I am not sure what else I need to do.

? You need to do what you are told to do: Draw several curves of the contour map! That has nothing to do with finding "domain" and range".
Graph x^3- y= -1.
Graph x^3- y= 0.
Graph x^3- y= 1.
Graph x^3- y= 2. etc.

 

[Office_Shredder]

A level curve is when f(x,y) is constant. So you're looking at $$x^3 - y = c$$ for some c a real number. Try starting with c=0, then see how to modify the level curve when c changes

 

[jheld]

Okay, I understand what you mean by making it equal that constant and then set the constant to a number of different values, but I'm having a difficult time putting the equation into a way that I can quasi-graph it.

 

[HallsofIvy]

Okay, I understand what you mean by making it equal that constant and then set the constant to a number of different values, but I'm having a difficult time putting the equation into a way that I can quasi-graph it.

Why "quasi-graph" it? Why not just graph them:

y= x³+ 1,
y= x³,
y= x³- 1,
y= x³- 2, etc.
can't be all that hard to graph!

 

[Office_Shredder]

You should be able to graph y = x³ in the plane at the very least

 

[jheld]

oh yeah, sorry that I didn't reply earlier. I graphed them with no problem. what I meant by 'quasi-graph' is that it is a contour graph, not the usual kind.

 

[HallsofIvy]

What do you see as a difference between a "contour map" and "the usual kind"?