Final answer:
The function z = (1 - x²)(1 - y²) represents a surface in 3D space and is calculated by substituting values for x and y into the equation and then performing the multiplication to find z.
Step-by-step explanation:
The function in question is z = (1 - x²)(1 - y²), which is a mathematical expression representing a surface in three-dimensional space. The function is a product of two binomials, one pertaining to the variable x and the other to the variable y. To evaluate this function, you would substitute numerical values for x and y and then perform the multiplication resulting in the value of z.
For example, if x = 2 and y = 2, substituting these values into the function would give z = (1 - 2²)(1 - 2²) = (1 - 4)(1 - 4) = (-3)(-3) = 9. Similarly, different values for x and y can be plugged into the formula to get the corresponding value of z.