Functions and Function Notation Any set of ordered pairs is known as a relation . A relation consists of an independent variable and a dependent variable . Usually, we think of x as the independent variable, and y as the dependent variable. The relation to the left consists of 6 ordered pairs. A function is a special kind of relations, in which each member of the independent variable is paired with one and only one value of the dependent variable. Is the relation to the left a function? Another way to state the definition of a function is that each member of the domain corresponds with exactly one member of the range . What is meant by domain and range?
Functions and Function Notation There are many ways to represent a function. Here are examples of three of the most common: A coordinate graph: A rule expressed symbolically or in words: “ The sale price is 20% off of the sticker price.” A list of ordered pairs: (3,5), (-1,8), (9,9), (-12, -1) -2 5 -5 0 1 1 6 4 -2 3 y x
Functions and Function Notation You have all seen function notation at some point in the past: If f ( x ) is defined as above, how would you evaluate f (-3)? How would you evaluate f (a+b)? f (watermelon)?
Are all relations functions? Consider the set of all points that are 3 units away from the point (2,2). What does a coordinate graph representing those points look like? What are the domain and range of this relation? This relation is not a function because for some members of the domain ( x values), there is more than one corresponding value in the range ( y values). You may recall the vertical line test .
<ul><li>Example: </li></ul><ul><li>The cost of renting a car is $35 per day plus $.40/mile for mileage over 100 miles. </li></ul><ul><li>Identify the dependent and independent variables. </li></ul><ul><li>State the domain and range of the function. </li></ul><ul><li>Write an equation for this function. </li></ul>