2.2 Functions

Relation a set of ordered pairs For Example A function is just a “special” relation

So what’s so special about a function? A function is a unique correspondence in which each element in the domain (x) corresponds to exactly one element in the range (y). Some elements in y may not be matched with an element in x. Two or more elements of x may be matched with the same y.

Are these relations functions?

Function Notation Input- xOutput- f(x) Example:

Piecewise Functions These are functions that are made up of “pieces” of other functions. For Example

Evaluate: when x = -1; x = 0; x = 1

Find the Domain of these Functions

Some Applications You work in the marketing department of a soft- drink company and are experimenting with a new soft-drink can that is slightly narrower and taller than a standard can. For you experimental can, the ratio of the height to the radius is 4. a)Express the volume of the can as a function of the radius r b)Express the volume of the can as a function of the height h

Another The money C (in billions of dollars) spent for direct mail advertising in the United States increased in a linear pattern from 1990 to Then, in 1993, the money spent took a jump, and until 1996, increased in a different linear pattern. These two patterns can be approximated by the function: where t=0 represents Use this function to approximate the total amount spent for direct mail advertising between 1990 and 1996.

Evaluating the Difference Quotient