Domain and Range Day 1 Revised ©2014, Viet.dang@humble.k12.tx.us 2/28/2019 8:59 PM Domain and Range

Definitions A relation is between two variables of x and y An ordered pair consist of a x and y–coordinate in brackets It may be viewed as ordered pairs, mapping design, table, equation, or written in sentences X–values can be known as inputs, domain, independent variable Y–values can be known as outputs, range, dependent variable 2/28/2019 8:59 PM Domain and Range

What is a Relation or a Function? What is a function? Can a function be a relation? Can a relation be a function? NO REPEATING X-Coordinates 2/28/2019 8:59 PM Domain and Range

Function Machine 2/28/2019 8:59 PM Domain and Range

“A doctor needs his or her ID to eXamine you” Definitions x y D R I “A doctor needs his or her ID to eXamine you” 2/28/2019 8:59 PM Domain and Range

Example 1 Is this relation a function? 2/28/2019 8:59 PM Domain and Range

Your Turn Is this relation a function? 2/28/2019 8:59 PM Domain and Range

Boys vs Girls a b c 1 2 3 a b c 1 2 3 Is this relation a function? 2/28/2019 8:59 PM Domain and Range

Example 2 3 1 –1 2 Would this mapping be considered a function? –1 2 2/28/2019 8:59 PM Domain and Range

Your Turn Would this mapping be considered a function? 2/28/2019 8:59 PM Domain and Range

What do these signs mean? > Greater than ≥ Greater than OR equal to < Less than Less than OR equal to ≤ 2/28/2019 8:59 PM Domain and Range

Definitions Inequality is an equation where the variable does not equal to each other >, <, or ≠ requires the dot being OPEN hole >, <, or = required the dot being CLOSED hole 2/28/2019 8:59 PM Domain and Range

To Write Inequalities Simple Inequalities (only ONE starting or ending point) Follow the arrow Variable Should always go first Compound Inequalities (more than ONE starting or ending point) Always use < or < in between the variable Smallest number ALWAYS comes first Biggest number ALWAYS comes last 2/28/2019 8:59 PM Domain and Range

Example 3 What is the domain and range? Write them in Compound Inequality form, if it is a function. 2/28/2019 8:59 PM Domain and Range

Example 4 What is the domain and range? Write them in Compound Inequality form, if it is a function. 2/28/2019 8:59 PM Domain and Range

Example 5 What is the domain and range? Write them in Compound Inequality form. 2/28/2019 8:59 PM Domain and Range

Example 6 What is the domain and range? Write them in Compound Inequality form, if it is a function. 2/28/2019 8:59 PM Domain and Range

Example 7 Identify the domain and range below. 2/28/2019 8:59 PM

Example 8 Identify the domain and range below. 2/28/2019 8:59 PM

Your Turn What is the domain and range? Write them in Compound Inequality form. 2/28/2019 8:59 PM Domain and Range

Vertical Line Test Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point. NO REPEATING X-COORDINATES “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function 2/28/2019 8:59 PM Domain and Range

Example 9 Would this graph be a function? 2/28/2019 8:59 PM Domain and Range

Example 10 Would this graph be a function? 2/28/2019 8:59 PM Domain and Range

Your Turn Would this graph be a function? 2/28/2019 8:59 PM Domain and Range

Example 11 Given g(x) = x2 – 3, determine g(2). (2)2 g(2) = 4 – 3 g(2) = 1 2/28/2019 8:59 PM Domain and Range

Example 12 Given f(x) = x2 – 2x + 4, evaluate f(–5). 2/28/2019 8:59 PM Domain and Range

Your Turn Given f(x) = x2 – 6x + 9, evaluate f(1/2). 2/28/2019 8:59 PM Domain and Range

Assignment Worksheet 2/28/2019 8:59 PM Domain and Range

Test Distribution 1st 2nd 6th 7th A 3 8 4 6 B 10 9 7 C 5 D 1 2 F No-Shows 100+ Range 59-100 42-100 48-94 52-97 Avg 79.91 77.71 76.29 78.04 2/28/2019 8:59 PM Domain and Range