Quiz (3ab) Last name Work is optional. Correct answer written on line 5 points,

Question

Quiz (3ab) Last name Work is optional. Correct answer written on line 5 points, no anwer is circled and nothing on the line 2 points, wrong answer 0 point. Write E, if the correct answer is not listed. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. First name Find the domain and range and describe the level curves for the function fix.y). 1) f(x y) - (-3x 2y)5 1) A) Domain: all points in the xy-plane; range: all real numbers; level curves: lines -3x -2y c B) Domain: all points in the xy-plane; range: real numbers z 0; level curves: lines-3x-2y = c, c 0 C) Domain: all points in the xy-plane; range: all real numbers; level curves: lines-3x-2y-c,c D) Domain: all points in the xy-plane; range: real numbers z z 0; level curves: lines-3x-2y = c

Explanation / Answer

We have f(x,y) = (- 3x - 2y)5

So our function is a polynomial function and we know that a polynomial function is defined for all real numbers. Hence the domain for f(x,y) is all real numbers.

Likewise the range of a polynomial function is all real numbers

=> The level curve for the function f(x,y) would be a straight line and the general equation would be :

- 3x - 2y = c

Hence Option (A) is correct

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