How do you graph this function?

[michonamona]

Homework Statement

For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z.

z = min(2x+1, x+y, 2y+1)

Homework Equations

The Attempt at a Solution

Ive been working on this for awhile, but I can't seem to get it right.

Thanks,
M

 

[Mark44]

Homework Statement

For a given fixed value, z, how would the level curves of the function below look like? (i.e. the graph of the function in the xy plane, for some given value z.

z = min(2x+1, x+y, 2y+1)

Homework Equations

The Attempt at a Solution

Ive been working on this for awhile, but I can't seem to get it right.

Thanks,
M

My take on this is that all three expressions on the right side of your equation above should be considered functions of x and y. The equations z = f(x, y) = 2x + 1, z = g(x, y) = x + y, and z = h(x, y) = 2y + 1 all represent planes in R³.

The function z = k(x, y) = min{f(x, y), g(x, y), h(x, y)} assigns to each point (x, y) in the domain, whatever number is the smallest of the three functions at that point.

Graphing each of the three functions would be a good start, IMO.