Transcript Tuesday, Oct 30 - Xenia Community Schools

5 Minute Check
Complete in your notebook. Fill in with < ,
> , or = to make the inequality true.
1. 302, 788
203,788
2. 892,341
892,431
Solve.
3. x + 44 = 90
4. 16m = 48
5 Minute Check
Fill in with < , > , or = to make the inequality
true.
1. 302, 788
203,788
5 Minute Check
Fill in with < , > , or = to make the inequality
true.
1. 302, 788 > 203,788
5 Minute Check
Fill in with < , > , or = to make the inequality
true.
2. 892,341
892,431
5 Minute Check
Fill in with < , > , or = to make the inequality
true.
2. 892,341 < 892,431
5 Minute Check
Solve.
3. x + 44 = 90
5 Minute Check
Solve.
3. x + 44 = 90
-44 = -44
x + 0 = 46
5 Minute Check
Solve.
4. 16m = 48
5 Minute Check
Solve.
4. 16m = 48
16m
16
=
48
16
m = 3
Thursday, Nov 20
Chapter 6.8.1/6.8.2
Function Tables
& Function Rules
Function Tables
Objective: Complete function tables and find
function rules.
Function Tables
A function is a relation that assigns exactly
one output value to one input value.
Function Tables
A function is a relation that assigns exactly
one output value to one input value.
Think of a function as an algebraic expression
with one variable (x).
Function Tables
A function rule describes the relationship
between each input and output.
Function Tables
A Function Rule is like a machine that has an
input and an output. And the output is
related somehow to the input.
Function Tables
A table that contains an input, output and
function rule is called a function table.
function rule
Function Tables
The input (x) values can be inserted into the
function rule.
Function Tables
The output (y) values can be inserted into the
determined by simplifying function rule.
Function Tables
Since the Function Rule is an expression that
describes how the x value goes to the y value,
it will only have an x variable.
Function Tables
The input (x) value is also known as the
independent variable.
(The input value can be any number)
Function Tables
The output (y) value is also known as the
dependent variable.
(The output value depends on the input value)
Function Tables
Complete the function table.
Do this on your own.
Function Tables
Complete the function table.
Function Tables
Sometimes the function table has the output
values and the function rule, and the input
values need to be determined.
We can do this by applying the inverse
operation of the function rule.
Function Tables
Complete the function table.
What is the inverse operation of the function
rule?
Function Tables
Complete the function table.
What is the inverse operation of the function
rule? Division.
2
5
7
Function Tables
Complete the function table.
We can complete the middle column by
substituting the number in for the variable (x).
2
5
3(2)
3(5)
7
3(7)
Function Tables
If there are two operations in the function rule,
we apply the inverse operations in the
reverse order of operations.
i.e apply the inverse of subtraction, before the
inverse of multiplication.
5
7
Function Tables
Complete the function table.
What operations do we have?
2
5
3(2)
3(5)
7
3(7)
Function Tables
Complete the function table.
(1 + 1) ÷ 2 = 12
5
3(2)
3(5)
7
3(7)
Function Tables
Complete the function table.
12
(3 + 1) ÷ 2 = 25
7
2(1)
3(2)- 1
3(5)
3(7)
Function Tables
Complete the function table.
12
2(1)
3(2)- 1
25
(5 + 1) ÷ 2 = 37
3(5)- 1
2(2)
3(7)
Function Tables
Complete the function table.
12
2(1)
3(2)- 1
25
37
3(5)- 1
2(2)
3(7)
2(3)
-1
Function Tables
Complete the function table.
Do this on your own.
12
2(1)
3(2)- 1
25
37
3(5)- 1
2(2)
3(7)
2(3)
-1
Function Tables
Complete the function table.
Do this on your own.
12
2(1)
3(2)- 1
25
37
3(5)- 1
2(2)
3(7)
2(3)
-1
Function Tables
The Gomez family is traveling at a rate of 70 miles
per hour. The function rule that represents this is
70x, where x is the number of hours. Make a table
to find out how many hours they have driven at 140
miles, 280 miles and 350 miles.
Do this on your own.
Function Tables
The Gomez family is traveling at a rate of 70 miles
per hour. The function rule that represents this is
70x, where x is the number of hours. Make a table
to find out how many hours they have driven at 140
miles, 280 miles and 350 miles.
Function Tables
The Gomez family is traveling at a rate of 70 miles per hour.
The function rule that represents this is 70x, where x is
the number of hours. Make a table to find out how many
hours they have driven at 140 miles, 280 miles and 350
miles.
Using the x and y values as ordered pairs a graph can be
constructed.
Function Tables
The Gomez family is traveling at a rate of 70 miles per hour.
The function rule that represents this is 70x, where x is
the number of hours. Make a table to find out how many
hours they have driven at 140 miles, 280 miles and 350
miles.
Function Rules
A sequence is a list of numbers in a specific
order.
Function Rules
Arithmetic sequences can be found by adding
or subtracting the same number to the
previous term.
i.e. ; 2, 4, 6, 8, 10…….
Function Rules
Geometric sequences can be found by
multiplying or dividing the previous term by
the same number.
i.e. 1, 3, 9, 27……….
Function Rules
We can determine if a sequence is arithmetic
or geometric by finding the difference
between terms.
Function Rules
State whether the sequence is arithmetic or
geometric, then find the next two terms in the
sequence.
0.75, 1.75, 2.75, 3.75……
Function Rules
State whether the sequence is arithmetic or
geometric, then find the next two terms in the
sequence.
0.75, 1.75, 2.75, 3.75……
1
1
1
Since the difference between the terms is the
same, it is arithmetic.
The next term will be 1 + 3.75= 4.75
Then 1 + 4.75= 5.75
Function Rules
State whether the sequence is arithmetic or
geometric, then find the next two terms in the
sequence.
1, 6, 36, 216……
Function Rules
State whether the sequence is arithmetic or
geometric, then find the next two terms in the
sequence.
1, 6, 36, 216……
5
30
180
Since the difference between the terms is
increasing, it is geometric.
The next term will be 6 x 216 = 1,296
Then 6 x 1296 = 7,776
Function Rules
We can write a sequence on a function table
with the value of the term being the output
and the position of the number being the
input.
The position (n) is just the number of the term
in order in the sequence.
i.e. n = 8, mean the 8th term of the sequence.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
The position
is just the
number of
term in the
sequence.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
How do we get from the position to the value of
term?
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
Either position # - 4 or position # ÷ 3
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
Either position # - 4 or position # ÷ 3
Which one works for the 2nd set of numbers?
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
The pattern is the position # - 4
Is this arithmetic or geometric?
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
The pattern is the position # - 4
It is arithmetic since it uses addition or subtraction.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
Do this on your own.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
The pattern is the position # ·5
It is geometric since it uses multiplication or
division.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
We can use n to represent the position, so the
pattern can be described as 5n.
5n is the function rule for this table.
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
What would be the value for the 10th term?
(when n = 10)
Function Rules
Describe the pattern and state whether the
sequence an arithmetic or geometric
sequence .
What would be the value for the 10th term?
5n, n = 10; 5·10 = 50
Function Rules
Find the function rule and state whether the
sequence an arithmetic or geometric
sequence .
Do this on your own.
Function Rules
Find the function rule and state whether the
sequence an arithmetic or geometric
sequence .
The function rule is 8n, and it is geometric.
Function Rules
Find the function rule and state whether the
sequence an arithmetic or geometric
sequence .
The function rule is 8n, and it is geometric.
What is the value for the 8th term?
Function Rules
Find the function rule and state whether the
sequence an arithmetic or geometric
sequence .
The function rule is 8n, and it is geometric.
What is the value for the 8th term?
8n, n = 8; 8·8 = 64
Function Rules
Find the function rule and determine the value
for the 10th term.
Do this on your own.
Function Rules
Find the function rule and determine the value
for the 10th term.
n+4
n = 10,
10 + 4 = 14
Function Rules
Find the function rule and determine the value
for the 12th term.
Do this on your own.
Function Rules
Find the function rule and determine the value
for the 12th term.
3n
n = 12,
3 · 12 = 36
Function Rules
Find the function rule and determine the value
for the 10th term.
Do this on your own.
Function Rules
Find the function rule and determine the value
for the 10th term.
6n,
n = 10,
6 · 10 = 60
Function Rules
Find the function rule and determine the value
for the 15th term.
Do this on your own.
Function Rules
Find the function rule and determine the value
for the 15th term.
n + 2,
n = 15,
15 + 2 = 17
Function Rules
Find the function rule and determine the value
for the 9th term.
Do this on your own.
Function Rules
Find the function rule and determine the value
for the 9th term.
2n,
n = 9,
2 · 9 = 18
Function Rules
The table at the right shows the
fee for overdue books at a library,
based on the number of weeks the
book is overdue. Write a function
rule to find the fee for a book that
is x weeks overdue.
Do this on your own.
Function Rules
The table at the right shows the
fee for overdue books at a library,
based on the number of weeks the
book is overdue. Write a function
rule to find the fee for a book that
is x weeks overdue.
Notice the fee values increase by 2, this
means it is multiplied by 2.
(but that is not all the function rule)
increase
Function Rules
The table at the right shows the
fee for overdue books at a library,
based on the number of weeks the
book is overdue. Write a function
rule to find the fee for a book that
is x weeks overdue.
2x + 1
Function Rules
The table shows the number of necklaces that
Ari can make, based on the number of hours
she works. Write a function rule to find the
number of necklaces she can make in x hours.
Do this on your own.
Function Rules
The table shows the number of necklaces that
Ari can make, based on the number of hours
she works. Write a function rule to find the
number of necklaces she can make in x hours.
2x + 3
Function Tables
Isaiah is buying jelly beans. In bulk, they cost
$3 per pound, and a candy dish costs $2.
The function rule, 3x + 2 where x is the
number of pounds, can be used to find the
total cost of x pounds of jelly beans and 1
dish. Make a table that shows the total cost
of buying 2, 3, and 4 pounds of jelly beans
and 1 dish.
Do this on your own.
Function Tables
Isaiah is buying jelly beans. In bulk, they cost $3
per pound, and a candy dish costs $2. The
function rule, 3x + 2 where x is the number of
pounds, can be used to find the total cost of x
pounds of jelly beans and 1 dish. Make a table
that shows the total cost of buying 2, 3, and 4
pounds of jelly beans and 1 dish.
.
Function Rules
Find the function rule and determine the value
for the 10th term.
Function Rules
Find the function rule and determine the value
for the 10th term.
n²;
n = 10;
10² = 100
Function Tables
u
Explain how to find the input given the
function rule and output.
Function Tables
u
Explain how to find the input given the
function rule and output.
To find the input, work backwards by
performing the reverse of the operation.
Function Tables
Agenda Notes
Homework –
Homework Practice 6.8.1 –
Questions 1, 2, 5 & 8
Homework Practice 6.8.2All Questions
Due Friday, Nov 21
Mid-Chapter 6.8 Quiz – Tuesday, Nov 25