10 An introduction to functions
A function is a relation in which each element in the domain (the inputs) of the relation corresponds on exactly one element in the range
(outputs) of the relation.
A function is a relation in which each input, or element in the domain of the relation, corresponds to exactly one output, or element in the
range of the relation. (Each input has exactly one output)
Ex. 1) determine whether a relation represents a function
a.) {(Terry, JoAnn), (Carrie, Dave), (Jennie, Andrew)} or {(2,4),(3,5),(4,6)}
Yes this relation is a function.
b.) {(Julie, Terry), (Julie, Mike)} or {(2,4),(2,6)}
Is not a function
Ex. 2) determine whether a relation represents a function. Give the domain and range.
a.) {(1,3),(-1,4),(0,6),(2,8)}
c.) {(0,3),(1,4),(4,5),(9,5),(4,1)}
If a relation is to be a function, then there can only be one Y – value associated with the one X – value.
Ex.3) determine whether an equation represents a function
Ex.3) determine whether an equation
shows y as a function of x.
Vertical line test:
A set of points in the xy–plane is the graph of the function if and only if every vertical line intersects the graph in at most one point.
Ex. 5) using the vertical line test