Question

what is an expression that describes the relationship between each input and output

Answer 1

mathematical relationship in which each input corresponds to the same terms. 

Answer 2

A function is a mathematical expression  that describes the relation between each input and output . for example F(x) = x+2 In this equation F(x) is your output and x is your input . 
If x=2 ; F(x) = 4 , If x= 3 ; F(x) = 5 .