File

9/8/2016
Created by Kenya Clo
WARMUP 9/(# π‘œπ‘“ π‘™π‘–π‘šπ‘π‘  π‘Ž π‘ π‘π‘–π‘‘π‘’π‘Ÿ β„Žπ‘Žπ‘  𝑝𝑙𝑒𝑠
π‘‘β„Žπ‘’ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‘π‘’π‘›π‘‘π‘Žπ‘π‘™π‘’π‘  π‘Ž π‘π‘’π‘Ÿπ‘ π‘œπ‘› β„Žπ‘Žπ‘ )
GOING OVER THE
GRAPHING
WORKSHEET…
Can you figure out the rules?
1) Input
Output
Garage
g
Baboon
o
Function
o
Kayak
a
Dinosaur
u
3) Input
Output = 2nd to last
letter of input
(the β€œpenultimate”
letter)
1
Denver
4
Jupiter
10
Zipper
Friends
Output
Lischwe
2
Iowa
3
Pretzel
2
Mathematics
4
Equation
Output
Activity
2) Input
4) Input
5
Output
Lime
g
Stop Sign
r
Basketball
o
26
Sky
b
6
Banana
y
Output = Place
in alphabet of
the first letter
of the input
Output = # of
vowels in the
input
Output = First
letter of the
color of the
input
Table of Contents
9
Analyzing Key Features of Graphs
p. 1
p. 2
p. 3
p. 4
p. 5
p. 6
p. 7
p. 8
p. 9
Consecutive Sums Project
Stacking Cups Problem
Converting Fractions and Decimals (1.1)
Roots (1.8 & 1.9)
Rational vs. Irrational (1.1)
What is a Function?
Function Notation
Graphing Functions
Analyzing Key Features of Graphs
ONE IMPORTANT
THING TO NOTICE…
Did any of your graphs turn out to NOT BE FUNCTIONS?
Objectives:
-Compare linear/nonlinear equations
-Describe important β€œkey features” of graphs
OKAY, NOW LOOK BACK
AT YOUR FUNCTION
GRAPHS…
Look at the ones that are linear and the ones that are
nonlinear
Why do you think this happened???
What do you think made them linear or nonlinear? Come up
with some conjectures.
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COPY:
Let’s explore what the graphs of different functions look
like…
Linear Equations
Nonlinear Equations
No exponent on the variable!!!
Exponents other than 1
None of these other things: οƒ 
Variable inside a square roots
Variable in a denominator
https://www.desmos.com/calculator
WHITEBOARDS!
Today, you are NOT getting the regular whiteboards, you are
getting the GRAPHING SHEETS.
Variable inside an absolute value
LINEAR OR
NONLINEAR?
𝒇(𝒙) = πŸ’π’™ + πŸ‘
Regular answers can go on the back. Graphs will go on the
coordinate plane.
Linear
LINEAR OR
NONLINEAR?
LINEAR OR
NONLINEAR?
𝒇(𝒙) = π’™πŸ βˆ’ πŸ’
𝒙
𝒇(𝒙) = + πŸ’
πŸ“
Nonlinear
Linear
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LINEAR OR
NONLINEAR?
πŸ”
𝒇(𝒙) = βˆ’ 𝟐
𝒙
Nonlinear
LINEAR OR
NONLINEAR?
LINEAR OR
NONLINEAR?
𝒇(𝒙) = π’™πŸ‘ + πŸ’π’™ βˆ’ πŸ‘
Nonlinear
LINEAR OR
NONLINEAR?
𝒇 𝒙 = 𝟏𝟎𝟎 βˆ’ 𝒙
𝒇(𝒙) = πŸ“π’™ βˆ’ πŸπ’™
Linear
Linear
LINEAR OR
NONLINEAR?
LINEAR OR
NONLINEAR?
πŸ‘
𝟏
𝒇 𝒙 =βˆ’ 𝒙+
πŸ’
πŸ•
𝒇(𝒙) = πŸ’ 𝒙 βˆ’ πŸ‘
Linear
Nonlinear
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LINEAR OR
NONLINEAR?
LINEAR OR
NONLINEAR?
𝒇 𝒙 = πŸπ’™ + 𝟏𝟎
𝒇(𝒙) = πŸ”
Nonlinear
Linear
LINEAR OR
NONLINEAR?
𝒇(𝒙) = πŸ’π’™ βˆ’ πŸ‘
LINEAR OR
NONLINEAR?
πŸ‘
πŸ” βˆ’ 𝒙 = 𝒇(𝒙)
πŸ’
Linear
𝟐
Nonlinear
LINEAR OR
NONLINEAR?
𝒇 𝒙 = πŸπ’™πŸ‘ βˆ’ 𝒙 + 𝒙 βˆ’ πŸ’ +
Nonlinear
πŸ‘
𝒙
LINEAR OR
NONLINEAR?
π’š = πŸ‘π’™ + 𝟐
Linear
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WHAT COULD BE SOME IMPORTANT
THINGS ABOUT THIS GRAPH?
KEY FEATURES OF GRAPHS
Increasing: Where the y-values go up (from left to
right)
Decreasing: Where the y-values go down (from left to
right)
X-intercept: Where the graph crosses the x-axis
Y-intercept: Where the graph crosses the y-axis
Slope: How steep the graph is
Increasing/Decreasing?
KEY FEATURES?
Both increasing
Which graph has a greater x-intercept?
Graph 1
Which graph has a greater y-intercept?
Graph 1
Which graph has a greater slope?
Graph 1
Graph 2
Graph 2
X-intercepts: -3 and 2
Y-intercept: -6
Increasing/Decreasing?
First decreasing, then
increasing
KEY FEATURES?
KEY FEATURES?
Increasing/decreasing?
Increasing/decreasing?
Always increasing
X-intercept?
-8
Y-intercept?
6
Describe the slope.
Increasing, then decreasing, then increasing, then decreasing, etc.
X-intercept?
βˆ’πŸπ…, βˆ’π…, 𝟎, 𝝅, πŸπ…
Y-intercept?
𝟎
Describe the slope.
The slope is not constant.
The slope is not constant.
Above and beyond answer:
the slope starts out very
steep, then gets gradually
less steep
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KEY FEATURES?
CHOOSE THE GRAPH
THAT IS:
Increasing/decreasing?
Always increasing
X-intercept?
None
Y-intercept?
About 1.5
Decreasing, then increasing, then decreasing
Has an x-intercept of 4
A
B
C
Describe the slope.
The slope is not constant. It
starts not very steep, then
gets steeper and steeper.
DRAW A GRAPH WITH
THE FOLLOWING
CHARACTERISTICS:
DRAW A GRAPH WITH
THE FOLLOWING
CHARACTERISTICS:
x and y-intercepts are both zero
Always increasing
Always decreasing
The slope changes
Slope doesn’t change
IS THIS POSSIBLE?
WHICH OF THESE ARE
POSSIBLE?
Draw a graph that is increasing, where the x-and y-intercept
are both 5.
To connect these two points,
A) A graph that is increasing only, which has an x-intercept
of -4 and a y-intercept of 6.
the graph must decrease!
B) A graph that is increasing, then decreasing, has xintercepts of 5 and -5, and a y-intercept of -9.
C) A graph that is increasing, then decreasing, then
increasing again, that has x-intercepts of -8, 2, and 7,
and a y-intercept of 4.
IMPOSSIBLE
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HOMEWORK
Key Features Half-Sheet
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