MACM 101 Lecture 16: Lecture 16 Part 2_ Functions
21 Dec 2018
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The set f(c) = { b b | b = f(a) for some a c } is called the image of c. Example: f({adams, rodriguez}) = {a} f({chou, goodfriend, stevens}) = {b,c,f} Let f: a b be a function and c a. A function : c b is called a restriction of f to c if (a) = f(a) for all a c. Example: let c = {chou, goodfriend, stevens}. Then the function is a restriction of f. Let c a and f: c b. Any function g: a b such that g(a) = f(a) for all a c is called an extension of f. Clearly, g: r z, and g(a) = a = f(a) for any integer a. Function is a relation, therefore we can use all methods of describing relations. Although the graph and the matrix are not very economical.
