Chapter 4 Unit Question How do we graph in algebra?
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Transcript of Chapter 4 Unit Question How do we graph in algebra?
Chapter 4
Unit Question
How do we graph in algebra?
Open Learning Logs
Date on Left…Section 4 – 8 on right
Warm – Up Section 4 – 8
Tell in which quadrant or on which axis the point lies…
X – coordinate Y - coordinate
Positive Negative
Negative Negative
Negative Positive
0 Positive
Positive Positive
Negative 0
Section 8
How do we calculate size changes in geometry?
Homework Clicky
Size change model for multiplication…
Let k be a nonzero number without a unit. Then
kx is the result of applying a size change of
magnitude k to the quantity x.
Types of size changes:
EXPANSION CONTRACTION
k > 1 OR k < -1 -1 < k < 1
“Outside the ones” “Between the ones”
-4 -3 -2 -1 0 1 2 3 4
Graph the points…
A = ( 0 , 2 )
B = ( 2 , 1 )
C = ( 3 , 5 )
EXPANSION BY 2
A’ = 2( 0 , 2 )
B’ = 2( 2 , 1 )
C’ = 2( 3 , 5 )
= ( 0 , 4 )
= ( 4 , 2 )
= ( 6 , 10 )
Graph counts by twos
Positive expansions get bigger!
Graph the points…
A = ( 0 , 2 )
B = ( 2 , 1 )
C = ( 3 , 5 )
EXPANSION BY -2
A’ = -2( 0 , 2 )
B’ = -2( 2 , 1 )
C’ = -2( 3 , 5 )
= ( 0 , -4 )
= ( -4 , -2 )
= ( -6 , -10 )
Graph counts by twos
Negative expansions get bigger and “do a double flip”
Graph the points…
A = ( 0 , 1 )
B = ( 2 , 1 )
C = ( 4 , 3 )
CONTRACTION of magnitude -½
A’ = -½ ( 0 , 1 )
B’ = -½ ( 2 , 1 )
C’ = -½ ( 4 , 3 )
= ( 0 , -½ )
= ( -1 , -½ )
= ( -2 , -1½ )
Graph counts by ones
Negative contractions get smaller and “do a double flip”
Frank receives time and a half for overtime. If his overtime rate is $28.28, what is his normal wage?
28.285.1 x5.1 5.1
85.18x
Frank’s Wage is experiencing an expansion of 1.5…
If we let x = Frank’s Wage
Then 1.5x = his overtime wage
Frank’s normal wage is about $18.85/hour
Since I love to photocopy, I take a picture of dimensions 6cm by 8cm, reduce by 60% and then enlarge by 125%.
What are the new dimensions?
1st do the reduction
60% = 0.60
6 • 0.60 = 3.6
8 • 0.60 = 4.8
The picture is 3.6cm by 4.8 cm
after the reduction
2nd do the expansion
125% = 1.25
3.6 • 1.25 = 4.5
4.8 • 1.25 = 6
The picture is 4.5 cm by 6 cm
after the expansion
Can we combine them?
Reduce 60% = -60
Enlarge by 125% = +125
-60 + 125 = +65%
We CANNOT combine
Percents this way!!!!
6 • 0.65 = 3.9
8 • 0.65 = 5.2
Homework
• Do HoffmaSheet 4 – 8