2A function f is one-to-one if for each x in the domain of f there is exactly one y in the range and no y in the range is the image of more than one x in the domain.A function is not one-to-one if two different elements in the domain correspond to the same element in the range.
3x1 y1 x1 y1 x2 y2 x2 x3 x3 y3 y3 One-to-one function NOT One-to-one DomainRangeDomainRangeOne-to-onefunctionNOT One-to-onefunctionx1y1y2x3y3Not afunctionDomainRange
4M: Mother Function is NOT one-one JoeSamanthaAnnaIanChelseaGeorgeLauraJulieHilaryBarbaraSueHumansMothers
5S: Social Security function IS one-one JoeSamanthaAnnaIanChelseaGeorgeAmericansSSN
6Is the function f below one – one? 101112131415161234567
7Theorem Horizontal Line Test If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one.
8Use the graph to determine whether the function is one-to-one.Not one-to-one.
9Use the graph to determine whether the function is one-to-one.
10The inverse of a one-one function is obtained by switching the role of x and y
11The inverse of the social security function JoeSamanthaAnnaIanChelseaGeorgeSSNAmericans
14Let f denote a one-to-one function y = f(x) Let f denote a one-to-one function y = f(x). The inverse of f, denoted by f -1 , is a function such that f -1(f( x )) = x for every x in the domain of f and f(f -1(x))=x for every x in the domain of f -1..