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(U3) Lesson 2 - Have A Good Altitude

Last updated over 2 years ago
24 questions
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:
  1. Laptop
  2. Pencil
  3. Binder
Please complete the Jump Start (activator). This is independent it should be silent.
Required
0

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.

Lesson Key Points:

- 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.
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1

How long was Carmen's trip on Ice Age Trail?

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1

What was Carmen doing during the first 5 hours of the trip?

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After the first 5 hours, what was carmen doing on the trip?

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During Carmen's trip, how long did it take her to reach the highest point of the mountain and what was that altitude?

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At what altitude does her trip start? Is this the only time that she reaches this altitude during the trip?

Lesson Key Points:

- 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.
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1

The domain would be the lowest to greatest x values in the continuous function.
Using Inequality: low \leq x \leq high
Using interval notation: [low, high]

What is the domain of the function representing Carmens trip?

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1

The range would be the lowest to greatest y-value in the continuous function.
Using Inequality: low \leq y \leq high
Using interval notation: [low, high]

What is the range of the function representing Carmens trip?

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1

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?

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1

What interval(s) below properly represents the interval(s) of decrease of Carmens trip?

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1

What ordered pair(s) represents the maximum of Carmen's trip?

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What ordered pair(s) represents the minimum of Carmen's trip?

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1

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?

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1

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?

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Specify the domain of the function

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Specify the range of the function.

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1

Specify the interval(s) where the function is increasing.

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Identify the coordinates for the minimum of this function.

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1

Identify the coordinates of the maximum of this function.

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1

Identify the coordinates of the y-intercept.

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Occurs at the point (18,0)

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Occurs at the point (7,10)

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Can be written as [0,18]

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On the intervals [0,3) & (7,18]