1. U2D2 Have out: Bellwork: Simplify the following expressions. a) b) c)
Assignment, pencil, red pen, highlighter, textbook, GP notebook
U2D2
Have out:
Bellwork:
Simplify the following expressions. a) b) c) d) +1 +1 +1 +1 +2 +2 +2 +2
total:

2. Did you remember to set up your page for today?
Exponents and Graphing Sequences
BB 12 – 21, Exponents WS
9/13/13

3. More Rules of Exponents
Add to your notes:
Power of a Quotient
Distribute the power to the numerator and denominator
Rule:
Examples:

4. More Rules of Exponents
Add to your notes:
zero exponent
Any base (except zero) raised to a zero exponent is 1
Rule: 1
Examples:
8,905,362,100,484,593,1780 1 1

5. More Rules of Exponents
Add to your notes:
negative exponent
Negative powers are made positive by moving the base to the opposite side (numerator or denominator)
Rules:
Examples:

6. Recall from the previous day...
(i) Sequence
(ii) Describe the pattern
(iii) Yes / No 10 14 a)
0, 2, 4, 6, 8, __, __, __ 12
Add 2
Yes b)
1, 2, 4, 8, __, __, __ 16 32 64
Multiply by 2
Yes c)
7, 5, 3, 1, __, __, __ –1 –3 –5
Subtract 2
Yes
Recall from the previous day... d)
0, 1, 4, 9, __, __, __ 16 25 36
Add next odd or next square No e)
2, 3.5, 5, 6.5, __, __, __ 8
9.5 11
Add 1.5
Yes f)
1, 1, 2, 3, 5, __, __, __ 8 13 21
Add the previous 2 terms No g)
27, 9, 3, 1, __, __, __
Divide by 3
Yes h)
40, 20, 10, __, __, __ 5
Divide by 2
Yes i)
3,–1 –3, –3, –1,3, 9, __, __, __ 17
Add next even number No 27 39 j)
–4 –1, 2, 5, __, __, __ 8 11 14
Add 3
Yes k)
3, 6, 12, __, __, __ 24 48 96
Multiply by 2
Yes l)
0, 1, 8, 27, 64, ___, ___, ___
125
Next cube No
216
343

7. Sequences Add to your notes Sequence: Initial Value: Generator:
A set of numbers in which the numbers have a prescribed order and are capable of being indexed by the natural numbers (e.g., 0, 1, 2, 3, 4, …)
In this class, we use the notation t(n) for sequences.
Initial Value:
The “ZERO” term in a sequence.
Represented by t(0).
Generator:
The operation that is done to each term to get the next term.

8. Add to your notes Example: n t(n) Initial term #  2  Initial value 12
 Initial value 1
3.5 2 5 3
6.5
Generator:
add 1.5 4 8
In this example, the sequence is written as:
t(n) =
1.5n + 2

9. No!!! We are graphing sequences, not lines and curves.
BB – 12
BOOKMARK the page in your notebook where you completed BB – 3!!! Make sure you have out today’s resource pages.
a) Fill in the tables on the resource pages for the sequences from BB–3 for parts (a), (b), (c), (e), (g), (h) (j), and (k).
Be careful!!! Make sure that you locate the correct resource page for each part.
b) Plot the points in each table on the separate set of axes on your resource pages.
Should the points be connected?
No!!! We are graphing sequences, not lines and curves.
c) Write the initial value and generator on each graph.

10. BB – 12
3 A
3 C
3 E
3 J
I.V. = 0
Generator = add 2

11. Work in your groups
on BB

12. BB – 12
3 A
3 C
3 E
3 J
I.V. = 0
I.V. = 7
I.V. = 2
I.V. = –4
Generator = add 2
Generator = subtract 2
Generator = add 1.5
Generator = add 3

13. BB – 12
3 B
3 G
3 H
3 K
I.V. = 3
Generator = multiply by 2
I.V. = 1
I.V. = 27
I.V. = 40
Generator = multiply by 2
Generator = divide by 3
Generator = divide by 2

14. a) Which graphs look alike? Groups of graphs that look alike include:
BB – 13
Discuss the similarities among the graphs in BB–12. Write down your observations in relation to the questions below.
a) Which graphs look alike?
Groups of graphs that look alike include:
a, e, and j
b and k
g and h
b) Which graphs had similar generators?
Groups of graphs that had similar generators:
a, e, and j
b and k
g and h
c) What is the significance of the initial value in each graph?
The initial value is the y–intercept.

15. BB – 14
The graphs you drew for problem BB–12 from sequences of points may be difficult to compare and contrast. One way to learn more about the patterns is to draw “staircases” between points and label the amounts of vertical change per one unit of horizontal change. Draw a staircase for each graph and briefly describe the pattern in the staircase numbers beneath each graph in problem BB–12.
For example, the sequence 1, 2, 5, 10, 17, … gives this table: n 1 2 3 4
t(n) 5 10 17
which in turn gives the graph at the right.
The staircases increase by 2 each time.

16. BB – 12
3 A
3 C
3 E
3 J
I.V. = 0
I.V. = 7
I.V. = 2
I.V. = –4
Generator = add 2
Generator = subtract 2
Generator = add 1.5
Generator = add 3
subtract 2
add 2
add 1.5
add 3

17. BB – 12
3 B
3 G
3 H
3 K
I.V. = 3 20
Generator = multiply by 2
I.V. = 1
I.V. = 27
I.V. = 40
Generator = multiply by 2
Generator = divide by 3
Generator = divide by 2 16 18 12 10 8 6 5 4 6
2.5 3 2 2
1.25 1
multiply by 2
multiply by 1/3
multiply by 1/2
multiply by 2

18. Finish today's assignment:
BB & exponents WS

19. Old Slides

20. BB – 12
3 D
3 F
3 I
3 L
I.V. = 0
Generator = cube

21. BB – 12
3 D
3 F
3 I
3 L
I.V. = 0
Generator = cube 19 7 1