Download P~es +1- SB - TeacherWeb

Te~+book R~ferencv
P~es
Unit I - Activity 2
Name:
Date:
+1- SB
Period:
Activity 2: Interval and Absolute Value Notation (GLEs: 1,8, 10,25)
This activity reviews how to express answers in roster and set notation and teaches
interval and absolute value notation.
In this activity students will review graphing linear functions using interval notation.
Draw the following on a number line:
BeHringer:
(l)x
E
{-2, 1,3, 4},
(2) {x: x> 4}
•
(3) {x: x < 2 or x ~ 5}
(4) {x : x > 3 and x < O}
(5) {x: x~5 and x:S; 8}
(6)
{x :
-3
:s;
(7) { x E ~ }
x
< 6}
Unit I - Activity 2
Five Ways to Write Solution Sets
Use the BeHringer to review three of the five ways to write solution sets:
(1) Roster Notation: Use when the solutions are finite or can be infinite if a
pattern exists such as {... , 2, 4, 6, ... }; however the answers are discrete and
not continuous. The three dots are called ellipsis and represent numbers that
are omitted, but the pattern is understood.
(2) Set Builder Notation: Use when the answers are continuous and
infinite. The notation in Bellringer 6 is an and situation similar to Bellringer
5. Try to identify the difference in the set notation {x : 0 > x> 3} and
notation used in Bellringer 4. (Note: and is for intersection and or is for
union)
#3
III
(3) Number Line: Use with roster notation using closed dots or set notation
using solid lines. In Algebra I an open dot for endpoints that are not included
such as in x > 2 and a closed dot for endpoints that are included such as in x
~ 2 were used. The symbolism in which a parenthesis" ( " represents an
open dot and a bracket" [ "represents the closed dot on a number line. Use
this notation to •draw the number line answers for Bellringers 3, 5, and 6.
[
III
}
5 ]8•
•
56
2
[
[
4) Interval Notation: Use intervals to write continuous, infinite sets with
the following guidelines:
(1) Bracket - indicates that the endpoint is included. Never use brackets with
infinity
(2) Parenthesis - indicates that the endpoint is not included
(3) u and n - Use the symbol u, union, for or statements and n ,
intersection, for and statements. Most and statements can be written as one
interval and rarely use n .
For e>'4h1plt..,
SihC.e.-
·,nter-va..! noto.t;on
5
Bf.-/1 rl·Yl~
wou..ld
is bi-tw€.e..Y\
a.r.d
Common and simp/€.r
8
4- has
¢.
ho
so/u...-hOt1
+h~
Be.! / r'-Y13er 5
f'he- (nter-vo../ [5) 8J is mor~
be...
thttn
Slhc~
2
Unit I - Activity 2
using (
-00 ,
8]
n [5, 00 ).
You Try:
Now rewrite all the Bellringers, 1-7, in interval notation.
Solutions:
(1)
(5)
(3)
(2)
(7)
(6)
(4)
(5) Absolute Value Notation:
Absolute Value Notation:
Define:
lal
0 therefore
= { -Qa ifIf aQ "< 0;
151~
5 and
I-51 ~
5.
You try: Solve Ixl = 8 and list the answers in set builder notation and roster
notation.
Solution:
Absolute Value as Distance: Define absolute value as the distance on a
numberline from a center point. For example, Ixl = 5 can be written verbally
as, "This set includes the two numbers that are a distance of 5 from zero."
You Try: Express the following absolute value equalities in roster notation,
set builder notation, on the number line, and verbally as distance.
3
Unit I - Activity 2
(1) Ixl = 7
(2)
Ix+ 21 = 8
(3) IX-41 = 5
Do you see a pattern?
Absolute Value Inequalities
•
Develop the meaning of lal < b from the definition of absolute value:
lal < b ~ a < b and -a < b :. a < b and a> -b. (and/ between)
•
Develop the meaning of lal > b from the definition of absolute value:
lal > b ~ a > b or -a > b :. a > b or a < -b. (or/beyond)
Unit I - Activity 2
You Try: I have changed"
= " in the previous examples with inequalities, now express the
following absolute value inequalities in set builder notation, on the number line, verbally as
distance, and in interval notation:
(1) Ixl $; 7
Set Builder:
Number Line:
Verbally as distance:
Interval notation:
(2)
Ix
+ 21 > 8
Set Builder:
Number Line:
Verbally as distance:
Interval notation:
(3)
Ix-41 $; 5
Set Builder:
Number Line:
Verbally as distance:
Interval notation:
B. Now we are going to go in the other direction. Change the following intervals to
absolute value notation. (Hint: It is easier to graph on the number line first, find the
center and distance, and then determine the absolute value inequality.)
5
Unit I - Activity 2
(2) (-3,3)
(1) [-8,8]
Graph:
~
~
Absolute Inequality:
Graph:
4r-<:-------
Absolute Inequality:
(4)( -00,4)
(3) [-2,8]
u(4,00)
Graph:
Graph:
Absolute Inequality:
Absolute Inequality:
~
(~ (~IJ)~Cp] U [~2)OO)
Graph:
~
Absolute Inequality:
6