Transcript The graph below represents Maria’s distance from home one

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
• 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.
2.
3.
4.
Domain:
Range:
Intercepts:
Increasing or
Decreasing?
5. Maximum or
Minimum?
Characteristics
1.
2.
3.
4.
Domain:
Range:
Intercepts:
Increasing or
Decreasing?
5. Maximum or
Minimum?
6. Horizontal Asymptote:
Classwork
Characteristics of Functions
Worksheet 5 problems
Homework
Characteristics of Functions
Worksheet 6 problems