warm up
DESCRIPTION
Tuesday, January 21 st. Warm Up. What is the domain and Range? Where is the graph positive?. EOCT Week 1 Winners . Week 2 EOCT-#1 . To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe? . - PowerPoint PPT PresentationTRANSCRIPT
Warm Up1. What is the
domain and Range?
2. Where is the graph
positive?
Tuesday, January 21st
EOCT Week 1 Winners
Week 2 EOCT-#1 To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which
graph models the cost of renting a canoe?
Quiz Scores/Answers
A Look Ahead Tuesday: Rate of Change-Linear Wednesday: Rate of Change-Exponential Thursday: Rate of Change word Problems Friday: Rate of Change word Problems
*TEST next Tuesday!
What words do you think of when you think of rate
of change?!?
Finding Rate of Change
1.Tables 2.Graphs 3.Equations 4.Word Problems
Group Discussion
How would you describe the DIFFERENCE between the rate of
change between:
Exponential &
Linear Functions
Linear
Exponential
ROCLinear
Rate of change=CONSTANT CHANGE ADDING OR
SUBTRACTING At any interval the rate of change will be
the same!
Exponential Rate of
Change=constant change by MULTIPLICATION
Rate of change depends on the interval you are looking at!
LINEAR Key Concepts
1. Slope=rate of change 2. Positive ROC=Increasing 3. Negative ROC=Decreasing 4. ROC of ZERO=Horizontal
line 5. ROC of UNDEFINED=vertical
Line
Determine if ROC is Postive, Negative, zero, undefined-
Graphs
N P
U 0
Determine if ROC is Postive, Negative, zero, undefined-
Equations 1. Y=8
2. Y=3x + 7
3. X= 8
4. Y=-3x + 7 N
PU
0
Determine if ROC is Postive, Negative, zero, undefined-Tables
x y
0 -10
1 -5
2 0
3 5
x y
0 7
1 7
2 7
3 7
x y
0 -10
1 -15
2 -20
3 -25
x y
7 -10
7 -5
7 0
7 5
P 0 N U
Important: Must solve for y!
Find the Rate of Change
1. Y = 2x – 10 2. Y = -5x + 4 3. 2x = 4y + 16 4. 2y + 6x = 24
Remember: Two
negatives=Positive- -=+
ALWAYS
yx
x y
1 -20
2 -30
3 -40
4 -50
x y
5 12
10 14
15 16
20 18
1. 2.
x y
2 -2
4 -6
6 -10
8 -14
x y
-10
20
-6 40
-2 60
2 80
3. 4.
Finding ROC from Graphs
RunRise
xy
I. Rise and Run
Rise= y axis
Run= x axis
What goes first?
You need to rise up
before you run
Finding Slope with a GraphFind the slope of the line
Begin at one point and count vertically to fine the rise.
• Up=Positive • Down=NegativeThen count horizontally to the
second point to find the run.• Right=Positive • Left= Negative
It does not matter which point you start with. The slope is the same.
(3, 2)
(–6, 5)
•
•
Rise 3
Run –9
Rise –3
Run 9
Begin at one point and count vertically to find rise.
Remember: up=____ down=___
•
•
Then count horizontally to the second point to find the run
Remember: right=____left=_____
Rise 2
Run –5
Rise –2
Run 5
You Try!
SUMMARY What type of function has a ROC that
can be described as a constant change adding or subtracting
How do you find the ROC in a linear equation?
How do you find the ROC in a linear table?
How do you find the ROC on a linear graph?