Maria's Bike Journey Graph Analysis
The graph below represents Maria’s distance
from home one day as she rode her bike to meet
friends and do a couple of errands for her mom
before returning home.
1.
What do the horizontal lines on the graph represent?
2.
Where in the graph shows her taking care of the 2
errands?
3.
Compare how she
traveled at the beginning
to how she traveled at the
very end.
4.
Create Maria’s story so
that it matches the graph.
MCC9-12.F.IF.4 (p. 51)
•
For a function
that models a relationship between two
quantities
,
interpret key features of graphs
and
tables in terms of the quantities,
and sketch graphs
showing key features
given a verbal description
of the relationship.
Key features include:
intercepts; intervals where the function is
increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries;
end behavior.
Characteristics of
Functions
Intercepts
Intercepts
•
x-intercept
– the point at which the
line intersects the x-axis at
(x, 0)
•
y-intercept
– the point at which the
line intersects the y-axis at
(0, y)
Find the x and y intercepts, then graph.
-3x + 2y = 12
Increasing, Decreasing, or Constant
Increasing, Decreasing, or Constant
•
Sweep from left to right and notice what
happens to the y-values
•
Increasing
goes up (L to R)
•
Decreasing
falls down (L to R)
•
Constant
is a horizontal graph
Continuous vs Discrete
Continuous vs Discrete
•
Continuous
has NO breaks
•
Discrete
has gaps or breaks
Extrema
Extrema
•
Maximum Point
– greatest value
of the function
•
Minimum Point
– least value of
the function
Domain & Range
Domain & Range
•
Domain
– all x-values of a function
•
Range
– all y-values of a function
Notation
Notation
•
Interval
–
represents an interval as a
pair of numbers. The numbers are the
endpoints of the interval. Parentheses
and/or brackets are used to show
whether the endpoints are excluded or
included
•
Set
– using inequalities to describe the
values
Asymptote
Asymptote
A line that a graph gets closer
and closer to, but never crosses
or touches
Characteristics
Characteristics
1.
Domain:
2.
Range:
3.
Intercepts:
4.
Increasing or
Decreasing?
5.
Maximum or
Minimum?
Characteristics
Characteristics
1.
Domain:
2.
Range:
3.
Intercepts:
4.
Increasing or
Decreasing?
5.
Maximum or
Minimum?
6.
Horizontal Asymptote:
Classwork
Characteristics of Functions
Worksheet 5 problems
Homework
Characteristics of Functions
Worksheet 6 problems
Maria's bike journey graph depicts her distance from home as she rode to meet friends and run errands before returning home. The graph shows her stops for errands, changes in direction, and her path back home. By interpreting the key features of the graph, such as intercepts and intervals, we can analyze how Maria's journey unfolded.
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Presentation Transcript
The graph below represents Marias distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home. 1. What do the horizontal lines on the graph represent? 2. Where in the graph shows her taking care of the 2 errands? 3. Compare how she traveled at the beginning to how she traveled at the very end. 4. Create Maria s story so that it matches the graph.
MCC9-12.F.IF.4 (p. 51) For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.
Characteristics of Functions
Intercepts x-intercept the point at which the line intersects the x-axis at (x, 0) y-intercept the point at which the line intersects the y-axis at (0, y)
Find the x and y intercepts, then graph. -3x + 2y = 12
Increasing, Decreasing, or Constant Sweep from left to right and notice what happens to the y-values Increasing goes up (L to R) Decreasing falls down (L to R) Constant is a horizontal graph
Continuous vs Discrete Continuous has NO breaks Discrete has gaps or breaks
Extrema Maximum Point greatest value of the function Minimum Point least value of the function
Domain & Range Domain all x-values of a function Range all y-values of a function
Notation Interval represents an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included Set using inequalities to describe the values
Asymptote A line that a graph gets closer and closer to, but never crosses or touches
Characteristics 1. Domain: 2. Range: 3. Intercepts: 4. Increasing or Decreasing? 5. Maximum or Minimum?
Characteristics 1. Domain: 2. Range: 3. Intercepts: 4. Increasing or Decreasing? 5. Maximum or Minimum? 6. Horizontal Asymptote:
Classwork Characteristics of Functions Worksheet 5 problems
Homework Characteristics of Functions Worksheet 6 problems
