function of several variables is a function where the domain is a subset
of R^{n} and range is
R.
To find the domain of a function of several variables, we look for zero
denominators and negatives under square roots:
First, the inside of the square root must be positive, that is x - y > 0second, the denominator must be nonzero, that is x + y 0 hence we need to stay off the line y = -x Putting this together gives {(x,y) | x - y > 0 and
y
-x}
The graph to the right shows the domain as the shaded green region. .
The topographical map shown below is of the Rubicon Trail. It represents the function that maps a longitude and latitude to an altitude.
Each curve represents a path where the z-coordinate (altitude) is a constant. Crossing many topo lines in a short distance represents a path that is very steep. Now lets make our own contour map of the function.
f(x,y) = y - x
We see that each topo line is a parabola and that the y-intercept gives the height. Below is a contour diagram of this function.
Names for the curves drawn are
Back to the Functions of Several Variables Page Back to the Math 107 Home Page |