Final Answer:
The function is g(x, y) = 2 - x² - y² - 2xy.
The function comprises quadratic terms ( -x² \) and ( -y² ), indicating parabolic shapes, and a cross-product term ( -2xy ) signifying interaction between x and y.
Step-by-step explanation:
The given function, ( g(x, y) = 2 - x² - y² - 2xy ), is a multivariable function involving the variables x and y. Breaking down the function, we have quadratic terms represented by ( -x² ) and ( -y² ), indicating the presence of parabolic shapes along the x and y axes. Additionally, the term ( -2xy ) introduces a cross-product term, showcasing the interaction between x and y.
Analyzing each component provides insights into the behavior of the function concerning its input variables. The quadratic terms suggest concave downward shapes along the x and y directions, while the cross-product term implies a connection between the variables. Understanding the structure of such functions is crucial in various mathematical and scientific applications.