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Slide 1
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Functions from Tables and Graphs
Slide 3
Determining Functions From Graphs To be a function, the graph
must pass the vertical line test. When a vertical line passes
through the graph, it should only touch one point at a time
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Example
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Describing Graphs of Linear Functions Positive Slope =
IncreasingNegative Slope = Decreasing
Slide 11
Linear and Proportional Relationships All graphs of linear
proportional relationships are functions because they form a
straight line. Proportional: Straight line through (0, 0)Linear:
Straight line Function
Slide 12
Nonlinear Relationships Many nonlinear relationships are
functions, but a graph or table may be needed to be sure. Function
Not a Function
Slide 13
Notes- Functions from Tables A function is when each input
(x-value) corresponds to exactly one output (y- value) In other
words, when you substitute (x) into an equation there is only one
possible answer (y)
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Identifying Functions From a Table Every x input can have only
one corresponding output.
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Example xy 12 26 34 42 58 xy 12 26 14 42 58 FunctionNot a
function
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Example xy 12 26 34 42 58 xy 12 26 14 42 58 FunctionNot a
function Two different outputs for the same input
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Try- is this a function? xy 110 28 36 28 52 xy 18 24 30 44 58
xy 12 26 34 42 30
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Lets Graph One to See Why Each x Must Have a Unique y xy 00 24
34 42 31
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Lets Graph One to See Why xy 00 24 34 42 31
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For the following set of points, determine if the relationship
is a function 1)(-2, 3); (4, 2); (-3, 2); (4, 0) 2)(1, 4); (-3, 5);
(1, 4); (-2, 5); (3, 5) 3)(-5, 4); (4, -5); (-4, 5); (5, 4)
Slide 21
Determine if the following is a function y = 2x y = 3x + 4
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Nope
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Determine if the following is a function by completing the
table and graphing y = x - 2 xy 0 1 2 -2
Slide 24
Determine if the following is a function by completing the
table and graphing y = x - 3 xy 0 1 2 -2
Slide 25
Writing the Rule for a Function
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Writing the Rule You need to look at the inputs and outputs in
the table to find a way to get from x to y that works for all
points. May be addition, subtraction, multiplication, or a
combination Write in the form y = mx + b
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Find the rule y = x + 3
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Find the Rule
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y = 3x
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Find the Rule What does the changing of signs tell us about the
rule?
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Find the Rule y = 2x + 2 How does is the value x = 0
helpful?
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Find the Rule A good trick is to find the difference or change
in x and y. That tells us what we are multiplying by
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Find the Rule 1 3 When the x value increases by 1, the y value
increases by 3. This tells us that x is being multiplied by 3 y =
3x ___
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Find the Rule
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Closure Get up and find a new partner Write the rule for the
following:
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Writing the Rule Given Two Points
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Rate of Change
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Find the rate of change The linear function goes through the
points (2, 4) and (4, 8)
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Find the rate of change The linear function goes through the
points (-3, 2) and (6, -1)
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Find the rate of change The linear function goes through the
points (-3, -5) and (-1, 3)
Slide 53
Writing a Linear Function From Two Points This is a skill we
need to revisit. Find the rate of change (slope) Find the y
intercept (initial position) by substituting one coordinate pair
into y = mx + b
Slide 54
Write the equation of a linear function that goes through the
points (-1, 1) and (1, 5)
Slide 55
Write the equation of a linear function that goes through the
points (-4, 1) and (4, -3)
Slide 56
Are You Serious Right Now?
Slide 57
Carnival Amber and Mark went to the carnival on the same day.
There is a flat fee to enter, and all games are the same price.
Mark played 7 games and spent $12 (7, 12) and Amber played 11 games
and spent $16 (11, 16). What is the rate of change (how much is
each game)? How much was the entrance into the carnival?
Slide 58
Kayaking Max and Ryder both rented kayaks and equipment on the
same day from the same company for a different length of time. The
company charges a flat fee to rent equipment and an hourly rate for
the kayaks. Max rented the kayak for 3 hours and paid $52. Ryder
rented the kayak for 7 hours and paid $112. What is the rate of
change (cost for one hour kayak rental)? How much was the equipment
rental?
Slide 59
Cell Phone Bill Marcy recently signed up for a cell phone plan
and has no idea how much she is paying per minute, but knows that
her bill consists of a monthly fee and a cost per minute. She
looked at her bills from the last two months and found that she
used 500 minutes and paid $75 one month (500, 75) and she used 750
minutes and paid $100 the other month (750, 100). What is the rate
of change (cost per minute)? What is the monthly fee?