Question

QUESTION 9 Find the domain and range and describe the level curves for the function f(x,y) y+10 1(x, y)s a.Domain: all points in the x-y plane excluding x O: range: all real numbers; level curves: parabolas y ex2-10 b. Domain all points in the xey plane; range: real numbersz 0: level curves: parabolas y- ex2- 10 Domain :all points in the x-y plane; range: all real numbors; levol curvos: parabolas y ex2-10 d. Domain all points in the x-y plane excluding x 0, range: real numbers z z 0; level curves: parabolas y -ex2-10

Answer 1

f(x,y) . Ч+ 10 r2

This function is a rational function and it is defined for all points in the plane except for which the denominator is zero

Thus, $x\neq 0$

For $x=1,f(1,y)=y+10$ which we can make equal to any real number

As

f(11 r-10) = (r-10) + 10 = r

Level curves are found by solving

1210 for C a constant y + с.т.-10 for c a constant T2

So that

And so we have
Domain - R2 excluding x-0, Range -R
and
Cr2-10 for C a constant
as level curves

Correct option is A)