The domain of a function of two variables is a subset of the
coordinate plane {(x,y)| x and y ∈R}.
The range of a real-valued function f is the collection of all real numbers f (x,y) where (x,y) is in the domain of f.
The graph of a function of two variables is the
collection of points (x,y,f (x,y)) in 3-space where (x,y) is in the domain
of f.
Demos
Domain and Range
Exercises
What is the range of the function f (x) = ax2 + cy2? (The answer will depend on the constants a and c.)
What is the range of the function f (x,y) = –x4 + 2x2 –y2 where the domain is all (x,y)? (Give reasons for your answer,
without using the words "partial derivative".)
What is the range of the function f (x,y) = –x4 + 2x2 – y4 + 2y2?
What is the range of the function f (x,y) = x2 + 2bxy + y2? (The answer will depend on the constant b.)
What is the range of the function f (x,y) = ax2 + 2bxy + cy2? (The answer will depend on the constants a, b, and c.)
