Download Algebra 2 Notes 2.1 Relations and Functions Definitions: Relation: A

Algebra 2
Notes 2.1 Relations and Functions
Definitions:
Relation: A pairing of two sets of numbers. The first value is the input or domain. The second value is the output
or range. Since the order of the pairings is important, the relation is frequently written as a set of ordered pairs, a table, a
graph or a mapping
Example 1: Representing Relations
Table
Ordered pair
(2,2)
x
(2,2)
(0,1)
(3,1)
Graph
Mapping diagram
Input
Output
y
Functions: A function is a relation in which each input has exactly one output. If any input value ( domain) is
paired with more than one output range, it is not a function.
Example 2: Tell whether the relation is a function. Explain your reasoning.
Input
Output
Input
Output
2
4
6
6
12
18
2
4
-4
x
-2
-1
0
1
3
y
-4
-4
-4
-4
-4
Vertical line test for a function: If the same input is paired with more than one output, the points will line up
vertically on a graph. A relation is a function if no vertical line intersects more than one point of the graph.
Example 3: Use a vertical line test to tell if the relation is a function.
Example 4: Graph an equation in two variables by plotting points
Graph the equation y  2 x  1
x
y
The function y  2 x  1 is a linear function because its graph formed a line. Its equation is in the form y  mx  b
Function notation renames y as f (x)
f ( x)  mx  b is read “the value of f at x”
Example 5: Tell whether the function is linear. Then evaluate the function at x  4
g ( x)  5 x  8
f ( x)   x 2  2 x  7
h( x ) 
12
2x  5
Write a rule for a function:
Tickets to a concert are available online for $35 plus a handling fee of $2.50. The total cost is a function of the number of
tickets bought. What function rule models the cost of the concert tickets?
Evaluate the functions for 4 tickets. For 10 tickets.