The graph below represents Marias distance from home one day as she rode her bike to meet friends...
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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.
Characteristics of Functions
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
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
Picture Example
Example:
Continuous vs Discontinuous
• Continuous has NO breaks
• Discontinuous has gaps or breaks
Picture Example of Continuous
Picture Example of Discontinuous
Discrete Function - A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers. (The points are not connected
Extrema•Minimum Point – least value of the function. Lowest Point.
•Maximum Point – greatest value of the function. Highest Point
Picture Example
Example
Domain & Range
• Domain – all x-values of a function
• Range – all y-values of a function
Picture Example
Ecample
AsymptoteA line that a graph gets closer and closer to, but never crosses or touches
Example
Characteristics1. 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:
ClassworkCharacteristics of
FunctionsWorksheet 5
problems
HomeworkCharacteristics of
FunctionsWorksheet 6
problems