Question

1. match graphs (a) and (b) in figure 21 with the functions (i) $f(x,y)=-x + y^{2}$ (ii) $g(x,y)=x + y^{2}$

Explanation:

Step1: Analyze the sign of the $x$ - term

For the function $f(x,y)=-x + y^{2}$, as $x$ increases, the value of $z=-x + y^{2}$ decreases (since the coefficient of $x$ is - 1). For the function $g(x,y)=x + y^{2}$, as $x$ increases, the value of $z=x + y^{2}$ increases.

Step2: Observe the direction of the surface along the $x$ - axis

In graph (A), as we move along the positive $x$ - axis, the surface is decreasing. In graph (B), as we move along the positive $x$ - axis, the surface is increasing.

Answer:

Graph (A) corresponds to $f(x,y)=-x + y^{2}$, Graph (B) corresponds to $g(x,y)=x + y^{2}$