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Section 3.4 Functions of 3 (or more) Variables

Although we won't do much with them in this course it is possible to define (real valued) functions in \(n\) variables where \(n\) is any natural number, that is functions of the form \(f:\mathbb{R}^n\rightarrow\mathbb{R}\text{.}\)

The function \(f(x,y,z)=x^2+y^2+z^2\) is a function of the form \(f:\mathbb{R}^3\rightarrow\mathbb{R}\) .

The function \(f(w,x,y,z)=2wx^2+yz+\frac{w}{(x+z)}\) is a function of the form \(f:\mathbb{R}^4\rightarrow\mathbb{R}\) .

Of course, for such functions geometric representations are somewhat impractical.