Lesson 4 – 3 Function Rules, Tables and Graphs Agenda Lesson 4 – 3 Function Rules, Tables and Graphs Warm up/Attendance Warm Up Review Notes – Function Rules Practice Review Homework – Page 191 Problems 40 to 45 all

Warm Up Homework – Page 191 Problems 40 to 45 all Find the domain and range of each relation. Determine if each relation is a function, using a mapping diagram 1. {(2, 3), (2, 5), (2, 6), (2, 4)} 2. {(3, 2), (5, 2), (6, 2), (4, 2)} 3 {(3, 3), (5, 5), (6, 6), (4, 4)} Homework – Page 191 Problems 40 to 45 all

Function Rule – an equation that describes a function Input Output Function Rule Domain – is the set of input values Range – is the set of output values

y = 3x + 4 output input 3x + 4 x = 4 x = 6 x = 2 4 16 2 10 y = 10 y = 22 y = 16 Input Output x y 6 22

Input Output x y 6 22 2 10 4 16

Function Notation – a function that uses f(x) for the output. Example: y = 3x + 2 becomes f(x) = 3x + 2 f(x) is pronounced “f of x” or “f is a function of x” The notation g(x) and h(x) also indicate functions of x Input values are called the independent variables Output values are called the dependent variables

Evaluating a function rule EXAMPLE 1a Evaluating a function rule Evaluate f(x) = –3x – 10 for x = 6 f(x) = –3x – 10 f(6) = –3(6) – 10 f(6) = –18 – 10 f(6) = –28

Evaluating a function rule EXAMPLE 1b Evaluating a function rule Evaluate the function rule f(a) = –3a + 5 to find the range of the function for the domain {-3, 1, 4} f(a) = –3a + 5 f(-3) = –3(–3) + 5 f(1) = –3(1) + 5 f(a) = –3a + 5 f(a) = –3a + 5 f(4) = –3(4) + 5 f(-3) = 9 + 5 f(6) = 14 f(1) = –3 + 5 f(1) = 2 f(6) = –12 + 5 f(6) = –7

EXAMPLE 3 Application Suppose your group recorded a CD, now you want to copy and sell it. One company charges $250 plus $3 per CD. The total cost P(c) depends on the number of CDs burned. P(c) = 250 + 3c 200 400 600 500 1000 1500 P(c) Number of CDs C P(c) = 250 + 3c (c, P(c)) 100 250 + 3(100) = 550 (100, 550) 200 250 + 3(200) = 850 (200, 850) 300 250 + 3(300) = 1150 (300, 1150) 500 250 + 3(500) = 1750 (500, 1750)

Class work – Please do now Page 190 Problems 2 to 18 even For problems 10 to 16 use the domain { -1, 0, 1} to make a table only Homework – Page 191 Problems 40 to 45 all

Lesson 4 – 3 Function Rules, Tables and Graphs Agenda Lesson 4 – 3 Function Rules, Tables and Graphs Day 2 Warm up/Attendance Warm Up Review Notes – Function Rules Practice Review Homework – Page 191 Problems 47 to 52 all

Homework – Page 191 Problems 47 to 52 all Warm Up Find the range for the given f(x) using the domain {-1, 1, 3} 1. f(x) = 2x – 4 2. f(x) = 5 – 3x Homework – Page 191 Problems 47 to 52 all

4 Graphing Functions EXAMPLE Graph the function y = │x│ + 1. Find the domain and range. x y Domain All real numbers Range {y: y > 1}

5 Identify Functions EXAMPLE Find the domain for each relation determine if the relation is a function. 1. y = 3x – 2 2. y = 1 3 + x 3. x = y2

Class work – Please do now Page 191 Problems 20 to 36 even Homework – Page 191 Problems 47 to 52 all