match each function with its contour plot. click on a graph to make it larger. darker areas represent lower…

match each function with its contour plot. click on a graph to make it larger. darker areas represent lower elevations and lighter areas represent higher elevations. 1. $f(x,y)=x - y^{2}$ 2. $f(x,y)=y - x^{2}$ 3. $f(x,y)=y + x^{2}$ 4. $f(x,y)=x + y^{2}$

match each function with its contour plot. click on a graph to make it larger. darker areas represent lower elevations and lighter areas represent higher elevations. 1. $f(x,y)=x - y^{2}$ 2. $f(x,y)=y - x^{2}$ 3. $f(x,y)=y + x^{2}$ 4. $f(x,y)=x + y^{2}$

Answer

Explanation:

Step1: Analyze $f(x,y)=x - y^{2}$

Set $f(x,y)=k$, then $x=y^{2}+k$. It is a parabola opening to the right. The contour lines will have a shape corresponding to right - opening parabolas.

Step2: Analyze $f(x,y)=y - x^{2}$

Set $f(x,y)=k$, then $y=x^{2}+k$. It is a parabola opening upwards. The contour lines will have a shape corresponding to upward - opening parabolas.

Step3: Analyze $f(x,y)=y + x^{2}$

Set $f(x,y)=k$, then $y=-x^{2}+k$. It is a parabola opening downwards. The contour lines will have a shape corresponding to downward - opening parabolas.

Step4: Analyze $f(x,y)=x + y^{2}$

Set $f(x,y)=k$, then $x=-y^{2}+k$. It is a parabola opening to the left. The contour lines will have a shape corresponding to left - opening parabolas.

Answer:

  1. B. $f(x,y)=x - y^{2}$
  2. A. $f(x,y)=y - x^{2}$
  3. C. $f(x,y)=y + x^{2}$
  4. D. $f(x,y)=x + y^{2}$