Relations and Functions Lesson 3-2 Relations and Functions You'll Learn how to Identify Functions Find the domain and range

Identify Functions A function is a special type of relation that pairs an input or (domain) value with exactly one Output or (range). Class-Grade relation Student-age relation Student Grade Student Age Bilal Peter Selma Ahmad Omer 80 85 96 Hamad Salim Sally Rania 12 24 17 31 Each input is paired with exactly one output so it’s a function.. an input is paired with more than one output so it’s not a function..

Ordered pairs Graph Table Mapping Diagram -2 2 3 A relation can be represented in different ways: Ordered pairs {(-2, -1), (2, 3), (3, -2)} Graph Table Mapping Diagram x y -2 -1 -1 3 -2 -2 2 3 (2, 3) 2 3 3 -2 (-2, -1) (3, -2)

Reason: there is NO repeated x-value Find the domain and range Determine the Domain and the range. Tell whether it’s a function. Explain From the Table x y Domain : { 2, 3, 4} 2 3 Range : { 3, 4, 5, 6} 3 4 3 It is NOT a Function 5 4 6 Reason: there is a repeated x-value. From ordered pairs {(3, 1), (5, -1), (4, 0), (6, 1)} Domain : { 3, 5, 4, 6} Range : { -1, 0, 1} It is a Function Reason: there is NO repeated x-value

The pencil crosses the graph exactly once. Therefore it’s a Function Vertical Line Test The vertical line test is used to determine if a graph is a function. If a vertical line passes through a graph more than once, then the graph is NOT function. The pencil crosses the graph exactly once. Therefore it’s a Function

The pencil crosses the graph more than once The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x-value.

The pencil crosses the graph more than once The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x-value.

From a graph Domain [-5 , 4] Range [-4 , 3] It is a Function x y (4, 3) Domain [-5 , 4] Range [-4 , 3] It is a Function Reason: It passes the vertical line test (-5, -4) x y Domain [-4 , 3] Range [-4 , 4] It is NOT a Function Reason: It Does NOT pass the VLT