Functions and Surfaces L.K. Norris

In your first two semesters of calculus you have studied functions of one independent variable f(x). For example, f(x) = exp(x), f(x) = sin(x) , Ly1JImZHNiI2I0kieEdGJSwoKiRGJyIiJCIiIkYnISIjIiIlRis= are all functions of one variable. We recall that in general the graph of f(x), namely the function x --> (x,f(x)) for x in some interval I is a curve in the xy-plane. For example, the graph of Ly1JImZHNiI2I0kieEdGJSwoKiRGJyIiJCIiIkYnISIjIiIlRis= is plot(x^3-2*x+4,x=-5..5,thickness=3,color=green);

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

This semester we will study functions that depend on 2 and 3 independent variables. DEF: A function f of two independent variables x and y is a rule that assigns to each pair of real numbers (x,y) in the domain D one and only one real number f(x,y) in the range R. Here are a few examples: f(x,y) = exp(x*y) , f(x,y) = sin(KiYsJkkieEc2IiIiIkkieUdGJUYmRiYsKCokRiQiIiNGJiokRidGKkYmISIiRiZGLA==) , f(x,y) =LCgqJkkieEc2IiIiJEkieUdGJSIiIyIiIiomRiRGKEYnRikhIiIiIiVGKQ== Similarly, some rules for functions of three variables x, y and z are: f(x,y,z) = exp(KihJInhHNiIiIiJJInlHRiRGJUkiekdGJEYl) , f(x,y,z) = sin(KiYsKEkieEc2IiIiIkkieUdGJUYmSSJ6R0YlRiZGJiwqKiRGJCIiI0YmKiRGJ0YrRiYqJEYoRitGJiEiIkYmRi4=) , f(x,y,z) =LCoqKEkiekc2IiIiJEkieEdGJUYmSSJ5R0YlIiIjIiIiKihGJEYpRidGKUYoRiohIiNJJHh5ekdGJUYqRiQiIiU= We want to study three things about such functions: Domain, Range and Graph.

Convention: If only the RULE for a function is given, then for DOMAIN we take the largest set on which the rule is defined. Not that for functions of 2 variables the domain is a subset of KiRJIlJHNiIiIiM=, while for functions of 3 variables the domain will be a subset of KiRJIlJHNiIiIiQ=. In determining the domain one looks for values of x that make the rule UNDEFINED in order to rule out certain regions. Here are some examples.

We first note that the exponential function is defined for all real numbers. We next note that x*y is always a real number as is x*y*z . Hence there are no points to "rule out" and so the domain of exp(x*y) is all of KiRJIlJHNiIiIiM= , while the domain of the function exp(x*y*z) is all of KiRJIlJHNiIiIiQ=.

Again begin by noticing that sin(x) is defined for all real numbers x. The function KiYsJkkieEc2IiIiIkkieUdGJUYmRiYsKCokRiQiIiNGJiokRidGKkYmISIiRiZGLA== is a rational function and is defined whenever the denominator LCgqJEkieEc2IiIiIyIiIiokSSJ5R0YlRiZGJyEiIkYn is not zero. Thus the DOMAIN of this function will be all points in KiRJIlJHNiIiIiM= except the points on the unit circle LCYqJEkieEc2IiIiIyIiIiokSSJ5R0YlRiZGJw== =1 . Similarly, the domain of the function KiYsKEkieEc2IiIiIkkieUdGJUYmSSJ6R0YlRiZGJiwqKiRGJCIiI0YmKiRGJ0YrRiYqJEYoRitGJiEiIkYmRi4= is all of KiRJIlJHNiIiIiQ= except the points where the denominator vanish, namely on the unit sphere LywoKiRJInhHNiIiIiMiIiIqJEkieUdGJkYnRigqJEkiekdGJkYnRihGKA==.

The range of a real-valued function of 2 or 3 variables is a subset of the real line R. To determine the range one imagines that the independent variables vary over the domain of the function and tries to read the range from the formulas. Here are some examples.

We note first that the range of the exponential function is the subset (0,SSlpbmZpbml0eUclKnByb3RlY3RlZEc=) of the real numbers if its argument varies over all real numbers. So looking at exp(x*y), fix x = 1 and let y vary from -infinity to infinity. Then x*y varies over all real numbers, so the range of exp(x*y) is (0,SSlpbmZpbml0eUclKnByb3RlY3RlZEc=). A similar argument holds for exp(x*y*z).

Recall the following definition from your first semester of calculus. DEF: The graph of a function f of one independent variable x is the set of all points in the xy-plane of the form (x,f(x)) for x in the domain of f. For example, the graph of the function f(x) = sin(x) is the well-known sine curve: plot(sin(x),x=0..4*Pi,thickness=3,color=blue);

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

As mentioned in the introduction above, we have the following: CHARACTERIZATION: The graph of f(x) is, generically, a curve in the xy-plane. We now generalize these ideas to functions of two independent variables. DEF: The graph of a function f of two independent variable x and y is the set of all points in 3-dimensional space of the form (x,y,f(x,y)) for (x,y) in the domain of f. Consider, for example, f(x,y) = 1. The graph is the set of points in 3-space of the form (x,y,1), which is in fact just the z = 1 plane, i.e. a SURFACE in 3-space. plot3d(1,x=-5..5,y=-5..5,axes=boxed);

6%-I%GRIDG6$%*protectedGI(_syslibG6"6%;$!"&""!$""&F-F*X,F(I)anythingGF&F([gl'!%"!!#\bm":":3FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF00000000000003FF0000000000000-I*AXESSTYLEGF%6#I$BOXGF%-I+AXESLABELSGF%6%I"xGF(I"yGF(Q!F(

Let's use plot3d to look at a few more general examples. plot3d(x^2+y^2,x=-5..5,y=-5..5,axes=boxed);

6%-I%GRIDG6$%*protectedGI(_syslibG6"6%;$!"&""!$""&F-F*X,F(I)anythingGF&F([gl'!%"!!#\bm":":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*AXESSTYLEGF%6#I$BOXGF%-I+AXESLABELSGF%6%I"xGF(I"yGF(Q!F(

We notice again that the graph is a surface in 3-space. FACT: Generically, the graph of a function of two variables f(x,y) is a SURFACE in 3-dimensional space. Here's one more example. plot3d(y^2-x^2,x=-5..5,y=-5..5,axes=boxed);

6%-I%GRIDG6$%*protectedGI(_syslibG6"6%;$!"&""!$""&F-F*X,F(I)anythingGF&F([gl'!%"!!#\bm":":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*AXESSTYLEGF%6#I$BOXGF%-I+AXESLABELSGF%6%I"xGF(I"yGF(Q!F(

The graph of this function yields a surface that looks somewhat like a western style "saddle" for a horse. If you look carefully at the graph you will see that the graph looks to have a local maximum along the y-axis, while it has a local minimum value along the x-axis. The graph of this function has what is called a "saddle point" - a generalization of the concept of "inflection point" for graphs of functions of one variable.