Match the function with its graph (labeled I-VI). Give reasons for your choices.

(a) $$f(x, y)=|x|+|y|v$$

(b) $$f(x, y)=|x y|$$

(c) $$f(x, y)=\frac{1}{1+x^{2}+y^{2}}$$

(d) $$f(x, y)=\left(x^{2}-y^{2}\right)^{2}$$

(e) $$f(x, y)=(x-y)^{2}$$

(f) $$f(x, y)=\sin (|x|+|y|)$$

## Discussion

## Video Transcript

So that wasn't after Joe scratched. The function is that they go to half, thank you. Why we called you three. So, first of foam, we noticed that the function x y here That's not the best on wax either. Why? So the x and Y on the free vory boast. So any value of the X and y were doesn't change developed. Is that so? This unthinkingly just He's just, uh, bland Dotty's. But allow Jew, uh, X Y plan on bathroom through that plant. So this bonehead you missed your choice. You can sue anybody of the x and Y, and just to make sure that for those that hear always equal to three. So we had to fix the tree here and we have free to choose any value for the x and y so I can choose his own for the X and so far, the why. And that's the simplest way to choose a room for the point on the plan. So we have only information here. You should be able to scared it now. So in the treaty, we have, uh, x y Zeph system here. So does it will be the axe. This will be the why. And this will be the Zet. So we have to locate the bones of the three will be this phone here. That would be 003 And we need to sketch the plan that will be below to the X Y plan. So the ex wife plan will be displaying here. Some will be the X Y plan on biology. This plan should be the plan that we can imagine would be this one. And this plan here will contend the porn Zozo tree here, and it doesn't stop under battering here, but it would extend for forever. Okay, so this plan here we have the function F thanks. Why in coaching tree and that's it.

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