Today's Learning Goal:
Introduce interval notation for specifying domain, range, and intervals of increase and decrease on continuous functions.
Interpret a story context from a graph of a function using the features.
Solidify understanding of features of functions in the context of graphing a common situation.
Reminders:
Continuous functions can have any value within a specific interval and values are connected. (measureable)
Features: Maximum/minimum, domain, range, x-intercept, y-intercept, Intervals of increase and decrease, zero rate of change, continuous, discrete, discontinuous, Rate of change
Today's Materials:
Laptop
Pencil
Binder
Please complete the Jump Start (activator). This is independent it should be silent.
Omar is filling up a pool for his friends and himself. The pool hold 14 gallons of water at most.
The pools starts off empty.
Omar started filling up the pool at a rate of 3 gallons per minute for 3 minutes.
Omar stopped filling the pool for 3 minutes trying to get the hose unclogged.
As soon as the 3 minutes had passed, the pool unplugged and started draining at 2 gallons per minute for 2 minutes.
He quickly plugged it back and he was able to fill the pool at the rate of 3 gallons per minute until it was full.
Sketch it on the graph. Label:
the maximum,
minimum,
increase,
decrease,
zero rate of change,
and y intercept.
- Interpret graphs and tables for the story it tells.
Carmen and her dog go on a hiking trip at Ice Age Trail every year. She records her altitude, in thousands of feet, over time, in hours.
Use the graph to answer the questions that follow.
How long was Carmen's trip on Ice Age Trail?
Specify the domain of the function
What was Carmen doing during the first 5 hours of the trip?
After the first 5 hours, what was carmen doing on the trip?
During Carmen's trip, how long did it take her to reach the highest point of the mountain and what was that altitude?
At what altitude does her trip start? Is this the only time that she reaches this altitude during the trip?
- Interpret graphs for the story it tells.
- Using proper notation to specify the domain, range, intervals of increase and decrease in interval notation for continuous functions, and ordered pairs representing the maximum, minimum, x- intercept and y-intercept.
Carmen and her dog go on a hiking trip at Ice Age Trail every year. She records her altitude, in thousands of feet, over time, in hours.
Use the graph to answer the questions that follow.
The domain would be the lowest to greatest x values in the continuous function.
Using Inequality:
Using interval notation:
What is the domain of the function representing Carmens trip?
The range would be the lowest to greatest y-value in the continuous function.
Using Inequality:
Using interval notation:
What is the range of the function representing Carmens trip?
Reminder! Only use the x values of each increasing, decreasing, or zero r.o.c segment.
What interval(s) below properly represents the interval(s) of increase of Carmens trip?
What interval(s) below properly represents the interval(s) of decrease of Carmens trip?
What ordered pair(s) represents the maximum of Carmen's trip?
What ordered pair(s) represents the minimum of Carmen's trip?
The y-intercept is where the function line intercepts or touches the y-axis. This is represented as a coordinate point (x,y).
What is the y-intercept of the function representing Carmen's trip?
The x-intercept is where the function line intercepts or touches the x-axis. This is represented as a coordinate point (x,y).
What is the x-intercept of the function representing Carmen's trip?
Specify the range of the function.
Specify the interval(s) where the function is increasing.
Identify the coordinates for the minimum of this function.
Identify the coordinates of the maximum of this function.
Identify the coordinates of the y-intercept.
Occurs at the point (18,0)
Occurs at the point (7,10)
Can be written as [0,18]
On the intervals [0,3) & (7,18]
