(U3) Lesson 3 - Floating Down the River

By JAMES TAYLOR

Last updated almost 2 years ago

16 Questions

Today's Learning Goal:
Solidify understanding of key features of functions by analyzing tables and graphs and use interval notation for specifying domain, range, and intervals of increase and decrease on continuous functions.

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.

Required

(5 minutes) Use the provided graph to label the following features:
maximum
minimum
y-intercept
x-intercept
domain
range
Intervals of increase, decrease and horizontal (zero change).
Use the image above as a reference example if needed.

As you work through today's work, keep in mind the key features of countinuous functions. Use the list below to guide your thinking.
Domain - from the lowest x-value to greatest x-value.

Range – from the minimum (lowest y-value) to the maximum (greatest y-value).

Maximum – look for where the function changes from increasing to decreasing or the endpoints for the greatest possible y value. 

Minimum – look for where the function changes from decreasing to increasing or the endpoints for the least possible y value. 

Interval of increase – mark where the y-values start to increase and stop increasing. Write the interval with the x-values at the beginning and end of that segment.

Interval of decrease – mark where the y-values start to decrease and stop decreasing. Write the interval with the x-values at the beginning and end of that segment.

Launch, Explore, Discuss 

Alondra, Maria, and Sierra were floating in inner tubes down a river, enjoying their day. Alondra noticed that sometimes the water was much deeper in some places than in others. Maria noticed there were times they seemed to be moving faster than at other times. Sierra laughed and said “Math is everywhere!” To learn more about the river, Alondra and Maria collected data throughout the trip.

(10 minutes) Part 1:
Here is Alondra’s data table about the depth of the water as they floated along.
Use the data that Alondra collected in the table to interpret the key features of this relationship.
If the endpoint is included in the interval, use brackets [ or ]
If the endpoint is not included in the interval, use parentheses ( or )
Intervals are always written from the smallest value to the greatest value.
Interval notation is only used to describe continuous intervals. Used when writing Increase, decrease, &  horizontal intervals and domain and range.

(5 minutes) Part 2:
Maria created a graph by collecting data on a GPS unit that provided the distance she had traveled over a period of time.

Describe the key features of the relationship shown in Maria’s graph. Intervals of increase and decrease, domain, range, maximum, minimum, and intercepts.

(15 minutes) Part 3:
Sierra looked at the data collected by her two friends and made several of her own observations.

State whether you agree or disagree with each observation. Be ready to explain your choice during whole class review. 

Reminder: Part 1: Depth/time data  and Part 2: GPS distance/time data