Download 4.6 Functions and Linear Equations

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Transcript
Trick or Treat
• Halloween was almost over, and Mr. Green had less than 20
candies left. When the doorbell rang, he thought he would give
all the candies away.
When he opened the door, there were two trick or treaters. He
wanted to give away the candies evenly, but he noticed that
when he divided the candies in two, there was one left over.
At that point, he saw another trick or treater behind the first two.
He tried to divide the candies evenly among the three of them,
but again one was left over.
Finally, another trick or treater came to his door, making it four
trick or treaters altogether. Mr. Green still had one candy left
over after dividing the left over candies in fours.
How many candies did Mr. Green have left when the doorbell
rang?
Trick or Treat
Solution
• Mr. Green had 13 candies left over.
13 is the only number under 20 that fits the
description (it is one more than 12, which
is evenly divisible by 2, 3, and 4).
Functions and Linear
Equations
Lesson 4-6
Function
• A relationship where one thing depends on
another.
• In a function you start with an input
number, perform an operation, and get an
output number.
INPUT
FUNCTION
RULE
OUTPUT
Function Table
• You can organize the input numbers,
output numbers, and function rule in a
function table.
• Lets Try an example
Example
• Suppose you earn $5
each week. Make a
function table to show
your total earnings
after 4 weeks.
Input
(# of
weeks)
1
Function Output
rule
(total
( x 5)
earnings)
5x1
5
2
5x2
10
3
5x3
15
4
5x4
20
Words to Know
• Domain= the input values
• Range= the output values
• In our example the domain would be written as
{ 1, 2, 3, 4 } and the range would be written as
{ 5, 10, 15, 20 }
• The domain or input represents the x value and
the range the y value. Together they form an
ordered pair.
Example
Function
rule
Output
x
X-3
y
1
1-3
-2
0
0-3
-3
-1
-1 - 3
-4
-2
-2 - 3
-5
Input
• Make a function table
and graph the
equation.
• y = x -3
• Domain = {1,0,-1,-2}
• Range = {-2,-3,-4,-5}
• Ordered pairs =
• (1, -2) (0, -3) (-1,-4)
(-2, -5)
Example
Function
rule
Output
x
2x
y
1
2(1)
2
2
2(2)
4
3
2(3)
6
4
2(4)
8
Input
• Make a function table
and graph the
equation.
• y = 2x
• Domain = {1,2,3,4}
• Range = {2,4,6,8}
• Ordered pairs =
• (1, 2) (2, 4) (3,6)
(4, 8)
Example
Input
• Make a function table
and graph the
equation.
• y = 2x -1
• Domain = {1,2,3,4}
• Range = {1,3,5,7}
• Ordered pairs =
• (1, 1) (2, 3) (3,5)
(4, 7)
x
Function
rule
Output
2x -1
y
1
2(1)-1 1
2
2(2)-1
3
2(3)-1 5
4
2(4)-1
3
7
Your Turn
• Make a function table and graph the
equation.
• y = -3x
Homework
• Complete Lesson 4-6 # 2-14 evens
• Test Friday, Lessons 4-5 and 4-6.
• Begin Studying and Practicing Now!