2-1 Relations & Functions M11.D.1.1.2: Determine if a relation is a function given a set of points or a graph M11.D.1.1.3: Identify the domain, range, or inverse relation

Objectives Graphing Relations Identifying Functions

Vocabulary A relation is a set of pairs of input and output values. You can write a relation as a set of ordered pairs. ex. {(2,1), (-3,0), (4,10), (9, -4)} Input Output

Graphing a Relation Graph the relation {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}. Graph and label each ordered pair.

Vocabulary The domain of a relation is the set of all inputs, or x-coordinates of the ordered pairs. The range of a relation is the set of all outputs, or y-coordinates of the ordered pairs.

Finding Domain & Range Write the ordered pairs for the relation. Find the domain and range. {(–4, 4), (–3, –2), (–2, 4), (2, –4), (3, 2)} The domain is {–4, –3, –2, 2, 3}. The range is {–4, –2, 2, 4}.

Vocabulary A mapping diagram links elements of the domain with the corresponding elements of the range. Ex. A mapping diagram for the relation {(-1, -2), (3,6), (-5, -10), (3,2)} -10 -2 2 6 -5 -1 3

Making a Mapping Diagram Make a mapping diagram for the relation {(–1, 7), (1, 3), (1, 7), (–1, 3)}. Pair the domain elements with the range elements.

Vocabulary A function is a relation in which each element of the domain is paired with exactly one element of the range.

Identifying Functions Determine whether the relation is a function. The element –3 of the domain is paired with both 4 and 5 of the range. The relation is not a function. {(-3,4), (-3,5), (2,5)} If its written as ordered pairs, look for x values that duplicate.

Using the Vertical-Line Test Use the vertical-line test to determine whether the graph represents a function. If a vertical line passes through at least two points on the graph, then the graph is not a function. If you move an edge of a ruler from left to right across the graph, keeping the edge vertical as you do so, you see that the edge of the ruler never intersects the graph in more than one point in any position. Therefore, the graph does represent a function.

Vocabulary You read the function notation f(x) as “f of x”. NOTE: this does not mean “f times x” When the value of x is 3, f(3), represents the value of the function at x = 3

Function Notation Find ƒ(2) for each function. a. ƒ(x) = –x2 + 1 ƒ(2) = –22 + 1 = –4 + 1 = –3 b. ƒ(x) = |3x| ƒ(2) = |3 • 2| = |6| = 6 c. ƒ(x) = 9 1 – x ƒ(2) = = = –9 9 1 – 2 –1

Homework Pg 59 # 1,2,5,6,8,9,12,13,16,17,22