Z2 are fixed. 8. Determine how the line x = 1 maps into the w-plane under the mapping w = f(z) = 1/z.

Sketch four contour lines and the graph of the function f: R²> R given by

Siven the function f(x.y) = In (6x. 3y), answer the following questions. Find the function's domain. Find the function's range. Describe the function's level curves. Find the boundary of the function's domain. Determine if the domain is an open region, a closed region, both, or neither. Decide if the domain is bounded or unbounded.

C) Write a function f(x, y) such that the domain of f(x, y) is D = {(z,y) | 2² 29-y²}. Also provide a sketch for the domain

Consider the function z = 4x²+4y²-4 z = f(x, y). Find equations for the xy-trace, xz-trace, and yz-trace for the graph of Find equations for the level curves f(x, y) = c for c= -3, 0, 1, 4. Then sketch and luoel these curves in the xy-plane (on the same set of axes).

Find the domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for which: - 3x2 (A) y (F) y s 1+ (G) y 2 * (H) y > 1+ 3x2 (Н) у >

Consider the function defined by f(x, y) = y + √x+2. (a) Find the domain and range of f. (b) Draw a contour map of f for k=-1,0,1. (c) Sketch the graph of J.