Functions — Formula Sheet

A relation f from a set A to a set B is a function if every element of A has exactly one image in B.

Domain of a function f:A→B is A; codomain is B; range is the set of all images of elements of A.

Number of functions from A to B = q^p

Constant function: f(x)=k

Identity function: f(x)=x

Polynomial function: f(x)=a0+a1x+...+anx^n

Rational function: f(x)=g(x)/h(x)

Linear function: f(x)=ax+b

Domain of f/g = {x: x in D1∩D2, g(x)≠0}

Domain of f+g = D1∩D2

Domain of fg = D1∩D2

Vertical line test: If any line parallel to the y-axis cuts the curve at no more than one point, the curve represents a function.

Horizontal line test: If any line parallel to the x-axis cuts the graph at no more than one point, the curve represents a one-one function.

If n(A) = p and n(B) = q, then number of functions from A to B is q^p.