input Juicer Machine output Juicer Machine This Machine

input Juicer Machine output Juicer Machine This Machine is functioning well (working good) Not-functioning well Each input gives exactly one output An input gives more than one output

Lesson 3 -2 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 Grade Bilal Peter 80 Selma 85 Ahmad 96 Student-Country relation Student Country Hamad Syria Salim UAE Sally Lebanon Rania Palestine Omer 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. .

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

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 3 3 4 Range : { 3, 4, 5, 6} 5 It is NOT a Function 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

Vertical Line Test: is a test used to determine whether a relation is a function or not. A graph is said to be a function if the vertical line drawn does not intersect the graph more than one point. x y (4, 3) (-5, -4) x y Domain -5 ≤ x ≤ 4 OR Range -4 ≤ y ≤ 3 OR [-5, 4] Domain -4 ≤ x ≤ 3 [-4, 3] Range -4 ≤ y ≤ 4 OR [-4, 3] OR [-4, 4] It is a Function It is NOT a Function Reason: It passes the VLT Reason: It Does NOT pass the VLT