1. 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

2. 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

3. 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

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

5. Input
Output x y

6. 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

7. 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

8. 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

9. 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) = c
500
1000
1500
P(c)
Number of CDs C
P(c) = c
(c, P(c))
100
(100) = 550
(100, 550)
200
(200) = 850
(200, 850)
300
(300) = 1150
(300, 1150)
500
(500) = 1750
(500, 1750)

10. 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

12. 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

13. 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

14. 4 Graphing Functions EXAMPLE
Graph the function y = │x│ Find the domain and range. x y
Domain
All real numbers
Range
{y: y > 1}

15. 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

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