11.1

Let g(x, y) = cos(x + 5y). (a) Evaluate g(10, −2). (b) Find the domain of g. (c) Find the range of g. (Enter your answer using interval notation.)

(a) g(10, −2) = 1 (b) R² (c) [-1,1]

Sketch the graph of the function. f(x, y) = y² + 4

Bent paper

Find and sketch the domain of the function. f(x, y) = √(3x − y)

Checker board

Find and sketch the domain of the function. f(x, y) = arcsin(x² + y² − 5)

Concentric circles

Draw a contour map of the function showing several level curves. f(x, y) = ye^(4x)

Converging lines

Draw a contour map of the function showing several level curves. f(x, y) = x³ − 5y

Layered, positive cubic functions

Find and sketch the domain of the function. f(x, y, z) = √(25 − x² − y² − z²)

Sphere

Describe the level surfaces of the function. f(x, y, z) = x + 2y + 4z

The level surfaces are a family of parallel planes.

Sketch the graph of the function. f(x, y) = 12 − 4x − 5y

Triangle