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For the 14.1 homework tonight, many of the problems ask you to describe the level curves of the function. I understand how to do the rest of the problem, but how does one visualize what the level curves will look like? Is a 3D graphing program necessary, or is it possible to look at the function and tell?

For example (#14.1.1), let $ f(x,y) = (x−y)^2$. The level curves of this function looks like lines of slope $1$... how could one tell that from the function alone?

For the 14.1 homework tonight, many of the problems ask you to describe the level curves of the function. I understand how to do the rest of the problem, but how does one visualize what the level curves will look like? Is a 3D graphing program necessary, or is it possible to look at the function and tell?

For example (#14.1.1), (Exercise 14.1.1), let $ f(x,y) = (x−y)^2$. The level curves of this function looks like lines of slope $1$... how could one tell that from the function alone?

For the 14.1 homework tonight, many of the problems ask you to describe the level curves of the function. I understand how to do the rest of the problem, but how does one visualize what the level curves will look like? Is a 3D graphing program necessary, or is it possible to look at the function and tell?

For example (Exercise 14.1.1), let $ f(x,y) = (x−y)^2$. The level curves of this function looks like lines of slope $1$... how could one tell that from the function alone?