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Lesson 9.4 Interpreting Graphs

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Warm Up
What are the 2 ways that you can determine if
something is a function?
For #’s 2 – 3, determine if it is a function, state the
domain, and the range.
2. {(2,4), (3, 6), (5,1), (4,4)}
3. {(-2 5), (-2,8), (5,9)}
For #’s 4 – 6, determine if it is a function. Why?
4.
5.
6. (zip code, city)
Lesson 9.4
Interpreting
Graphs
BOOM!
BOOM!
OBJECTIVES:
1. Describe, read, and interpret graphs of
real-world situations.
2. Make appropriate graphs of real-world
situations.
Linear vs. Nonlinear
• What does • As x increases at a
it mean if a constant rate, the
function values change
function is
at a constant rate.
linear?
Linear vs. Nonlinear
• What does • As x changes at a
it mean if a constant rate, the
function values change
function is
at a varying rate.
non-linear?
Examples:
Decide if the following situations
would be represented by a
linear or non-linear function.
1) For every hour you baby-sit,
you receive $5 in pay. linear
2)The temperature of a hot meal
and the number of minutes it
sits on the table without being
eaten. Non-linear
Types of movement
In real life graphs, the graph can only do three
things.
The graph can rise or grow.
The graph can fall or go down.
The graph can stay the same.
There can be a combination of the three movements,
but only one movement at a time, ie, you can’t be
growing and shrinking at the same time.
Increasing Graphs
Technical Definition: As the x values increase,
the y values also increase.
Example
One important thing
to remember about
graphs is how fast
they are rising or
falling. This changes
how “steep” the
graph is.
More Examples
Here are some other types of Increasing
graphs.
Real life situations
When you get to Calculus you can worry about
actual numbers, but for this class we are just
interested in the “general idea” of what the
graph is doing.
Dependent
Hint: A helpful way to read
these graphs is to use the
“as…then…” statement. The
bottom label (x value- the
independent variable) goes after
the as and the left label (y
value – the dependent variable)
goes after the then.
Independent
For example:
This graph could be
several real life
situations.
It could be earnings for
time worked at
Subway.
Or it could be a
man’s
distance away
from his
house as he is
walking.
How about the
crazy level of
Mrs. Falkner?
Your Turn
Come up with your own
stories for the following
graphs.
Hint: When writing
your own story, you
have to take into
account the
steepness of your
graph. Is your
story happening
fast or slow?
Decreasing
Graphs
Definition: As the x value increases, the y
value decreases.
Examples:
All of the graphs are decreasing:
some are decreasing quickly, others are
decreasing slowly.
Examples
Temperature
of liquid as
it cools.
Population of
rabbits after a
forest fire.
Your Turn
Come up with your own
stories for the following
graphs.
Constant Graphs
Definition: As the x value increases,
the y value stays the same.
Basically, any time the graph
flattens out
Now put it all together…
What would the graph look like for
the following story. Sketch it on
your paper.
Miss Palomaa is on a scavenger hunt!
She jumps in her Ford Echo to get
away first. She speeds up very
quickly, then has to slam on the
brakes to turn a corner, she
speeds up again only to come to a
full stop outside a Starbucks so
she can buy some coffee.
Fortunately for her the Starbucks
cup is also first on her list. Sketch
her car’s speed as time passes.
Classwork…Comic Strips
You will choose a comic strip
template and then draw a story in
the boxes…in the last big box you
will draw a graph of what was
happening in your story. Make
sure you have an independent (x)
and dependent variable (y).
Summary
The differences between an increasing
graph and a decreasing graph are…
Class work: Comic Strips
Homework: Worksheet 9.4
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