Assignment, pencil, red pen, highlighter,
textbook, GP notebook, calculator
Complete the tables and write the rule for each
of the following sequences.
1) The sequence is arithmetic.
2) The sequence is geometric.
n
0
1
2
3
4
n
0
1
2
t(n)
15
13
11
9
7
t(n)
4
12
36
+2
d  11 7  4  2
2  4 2
+2
t(n) = b(m)n
t(n) 2n 15
t(n) = 4(3)n
+2
+2
total:
12
4
108 324
m
+1
+1
3
m
324 = 36 m m
324 = 36(m)2 +1
36
36
9 = (m)2
9=
m2
3 = m +1
Interval notation can be a more efficient way of expressing domain
and range. Interval notation uses the following symbols:
Symbol
Represents
U
( )
The union of two or more sets
An open interval (i.e., do not include the endpoints)
[ ]
A closed interval (i.e., include the endpoints)
Set Notation Vs.
{ x | –2 < x  5 }
{ x | 10 < x <  }
{x|x0}
{x|x=9}
Interval Notation
( –2, 5 ]
(10,  )
(–, 0) U (0, )
[ 9]
Let’s try the first few problems on
today’s worksheet.
Domain, Range, & Functions Worksheet
y
1.
10
–5
y
2.
5
–10
x
3.
10
–5
5
–10
x
y
10
–5
5
–10
D: (set notation) {x| –1 < x ≤ 3}
{x| –3 ≤ x ≤ 5}
{x| –5 < x < 3}
(–1, 3]
D: (interval)
R: (set notation) {y| –7 ≤ y < 6}
[–7, 6)
R: (interval)
[–3, 5]
{y| –5 ≤ y ≤ 8}
[–5, 8]
(–5, 3)
{y| –2 < y ≤ 9}
(–2, 9]
x
Now, we are going to work with
How many of you like working with fractions???
Suppose there was a way to eliminate fractions from
an equation that you are trying to solve. Wouldn’t that
make it easier to do???
This is known as
Fraction Busters
2
x  6  10
3
To rewrite this equation without the
fraction, we ask ourselves , “How
can we eliminate the three?”
Fraction Busters uses the Multiplication Property of
Equality (that is we can multiply both sides of the equation
by the same number and still maintain equality) to rewrite
the equation without the fraction.
Start by multiplying the 3 with EVERYTHING
on BOTH SIDES of the equation.
2
x  6  10
3
2 
3 x   36  310
3 
2x 18  30
2x  12
x6
Multiply everything by 3.
Simplify and solve
Fraction Busters
Now for two more challenging examples. . .
1)
x 2x

5
6 3
 x  2 2 x 
6   6   65
6  3 
x  4x  30
5x  30
x6
2)
6 3
 1
x 4
6
3
4 x   4 x   4 x1
 x
4
24  3x  4x
24  x
Clear your desk except for pencil,
highlighter, and a calculator!
After the quiz, work on
the worksheet.
Old Slides
Resources
http://cnx.org/content/m13596/latest/
http://www.biology.arizona.edu/biomath/tutorials/Notation/SetBu
ilderNotation.html
http://www.analyzemath.com/DomainRange/DomainRange.html
http://www.phsmath.org/Alg1/pdfs/Lessons/L82.84.87.pdf
http://www.montgomerycollege.edu/faculty/~jriseber/public_ht
ml/160W1-3S05.pdf
Don’t copy…
The notation that we have been using for domain and range is called
set builder notation. In this notation, curly parentheses and variables
are used to express domain and range.
{ x | –2 < x  5 } means “the set of all real numbers x
such that x is greater than –2 and
less than or equal to 5.”
x is greater than –2 and less
The set of all
than or equal to 5
“such that”
real numbers x
{x|x0}
Means “the set of all real numbers x such
that x is not equal to zero.”
Find the domain using set builder notation and
interval notation.
x
1)
-3 -2
-1
0
1
2
3
4
5
6
7
8
Set builder: {x | –3 < x ≤ 5 }
( –3, 5 ]
Interval:
2)
x
-3
-2
-1
0
1
2
3
4
5
6
7
8
Set builder: {x | 1 ≤ x <  }
Interval: [ 1,  )
x
3)
-3 -2
-1
0
Set builder: {x | – < x <  }
Interval: ( –,  )
1
2
3
4
5
6
7
8