Section 3.6 Functions

Understanding Relations A relation is any set of ordered pairs. x y 1 2 3 4 1 2 3 4 y “depends” on the value we put in for x. Independent variable x 3 3 y 4 2 Dependent variable

Example State the domain and range of the relation. {(3, 5), (10, 12), (11, 8), (13, 15), (9, 12)} The domain consists of all the first coordinates in the ordered pairs. The range consists of all the second coordinates in the ordered pairs. The domain is {3, 9, 10, 11, 13}. The range is {5, 12, 8, 15}. We list 12 only once.

Function A function is a relation in which no two different ordered pairs have the same first coordinate. x y 1 2 3 4 1 2 3 4 Domain x 3 3 y 4 2 Range

Example State the domain and range of the relation and determine whether the relation is a function. {(2, 4), (5, 4), (3, 8), (2, 6), (1, 7)} Domain {(2, 4), (5, 4), (3, 8), (2, 6), (1, 7)} Range This is NOT a function because two different ordered pairs have the same first coordinate. The domain is {2, 5, 3, 1}. The range is {4, 8, 6, 7}.

Example Graph y = x2. Begin by constructing a table of values. x 2 y = (2)2 = 4 4 1 y = (1)2 = 1 1 y = (0)2 = 0 y = (1)2 = 1 2 y = (2)2 = 4 Plot the ordered pairs and connect the points with a smooth curve.

Example Graph y = x2 + 3. Begin by constructing a table of values. 2 (2)2 + 3 7 1 (1)2 + 3 4 (0)2 + 3 3 1 (1)2 + 3 2 (2)2 + 3 Plot the ordered pairs and connect the points with a smooth curve.

Example Graph x = y2 + 2. Begin by constructing a table of values. 2 (2)2 + 2 6 1 (1)2 + 2 3 (0)2 + 2 2 1 (1)2 + 2 (2)2 + 2 Plot the ordered pairs and connect the points with a smooth curve.

Vertical Line Test If a vertical line can intersect the graph of a relation more than once, the relation is not a function. If no such line can be drawn, then the relation is a function.

Example Determine whether each of the following is the graph of a function. a. b. c. x y x y x y Function Not a Function Not a Function

Example If find each of the following. a. f(2) b. f(4) c. f(0)