BELLRINGER:
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.
Review HW
Characteristics of
Functions
Coordinate Algebra
UNIT QUESTION: How can we use real-world
situations to construct and compare linear and
exponential models and solve problems?
Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5
Today’s Question: What are the key features of
a linear and an exponential function?
Standards: F.IF 4, F.IF 5, F.IF 7, F.IF 7a, F.IF 7e
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
• Minimum Point – least value of
the function
• Maximum Point – greatest 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?
Characteristics
1.
2.
3.
4.
Domain:
Range:
Intercepts:
Increasing or
Decreasing?
5. Maximum or
Minimum?
6. Horizontal Asymptote:
Characteristics
1.
2.
3.
4.
Domain:
Range:
Intercepts:
Increasing or
Decreasing?
5. Maximum or
Minimum?
6. Horizontal Asymptote:
Classwork
Characteristics of Functions
Worksheet 7 problems
Homework
Characteristics of Functions
Worksheet 6 problems