AgendaLesson 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

Find the domain and range of each relation. Determine if each relation is a function, using a mapping diagram

Homework – Page 191 Problems 40 to 45 all

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)}

Input

Output

FunctionRule

Function Rule – an equation that describes a function

Domain – is the set of input values

Range – is the set of output values

x = 6x = 4y = 10

x = 2

y = 3x + 4

output input

Input Output

x y

2 10

6 22

y = 16

4 16

y = 223x + 4

Input Output

x y

6 22 4 16 2 10

Function Notation – a function that uses f(x) for the output.

The notation g(x) and h(x) also indicate functions of x

f(x) is pronounced “f of x” or “f is a function of x”

Input values are called the independent variables

Output values are called the dependent variables

Example: y = 3x + 2 becomes f(x) = 3x + 2

EXAMPLE1a Evaluating a function rule

f(x) = –3x – 10

f(6) = –3(6) – 10

f(6) = –18 – 10

f(6) = –28

Evaluate f(x) = –3x – 10 for x = 6

EXAMPLE1b Evaluating a function rule

f(a) = –3a + 5

f(-3) = –3(–3) + 5

f(-3) = 9 + 5

f(6) = 14

f(1) = –3 + 5

f(1) = 2

f(a) = –3a + 5

f(4) = –3(4) + 5

f(6) = –12 + 5

f(6) = –7

Evaluate the function rule f(a) = –3a + 5 to find the range of the function for the domain {-3, 1, 4}

f(1) = –3(1) + 5

f(a) = –3a + 5

EXAMPLE3 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

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)

200 400 600

500

1000

1500

P(c)

Number of CDs

Class work – Please do nowPage 190 Problems 2 to 18 even

Homework – Page 191 Problems 40 to 45 all

For problems 10 to 16 use the domain { -1, 0, 1} to make a table only

AgendaLesson 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

Warm Up

Find the range for the given f(x) using the domain {-1, 1, 3}

Homework – Page 191 Problems 47 to 52 all

1. f(x) = 2x – 4 2. f(x) = 5 – 3x

EXAMPLE4 Graphing Functions

Graph the function y = │x│ + 1. Find the domain and range.

x y DomainAll real numbers

Range{y: y > 1}

EXAMPLE5 Identify Functions

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 nowPage 191 Problems 20 to 36 even

Homework – Page 191 Problems 47 to 52 all