Answer
See explanation
Work Step by Step
Step 1 A function \(f(x, y)\) takes two inputs, \(x\) and \(y\), and produces a unique value. By extending this into 3D space (\(xyz\)), we can assign the value of the function as \(z = f(x, y)\), meaning there's a unique \(z\) value for every combination of \(x\) and \(y\) values. Step 2 To visualize the function \(f(x, y)\), you can use three-dimensional graphs or contour plots. Generating a 3D graph involves plotting points \((x, y, z)\) on a function, resulting in a 3D surface. While this method helps in understanding the global behavior of the function, identifying exact values and the domain is relatively challenging. Step 3 An alternative method is generating contour plots. These plots are constructed by plotting functions \(z_k = f(x, y)\) on a 2D plane, where \(z_k\) is within the range of the function \(z = f(x, y)\). Geometrically, this is akin to taking horizontal cross-sections of the function \(z = f(x, y)\). Contour plots provide a clearer view of the values of the function and its domain, but they make it more challenging to infer the global behavior of the function
