M 6 LSN 4 Increasing and Decreasing Functions

M 6: LSN 4 Increasing and Decreasing Functions Lesson 4 Page S. 19 Read through each of the scenarios and choose the graph of the function that best matches the situation. Explain the reason behind each choice. Tie to LO

M 6: LSN 4 Increasing and Decreasing Functions Exercise 1 - Continued Scenario: c Explanation: The amount of water in the tub does not change over time; it remains constant. CFU

M 6: LSN 4 Increasing and Decreasing Functions Exercise 1 - Continued Scenario: b Explanation: The bathtub is being drained. So, the amount of water is decreasing, which means that the slope of the line is negative. The graph of the function also shows that there are initially �� 0 gallons of water in the tub. CFU

M 6: LSN 4 Increasing and Decreasing Functions Exercise 1 - Continued Scenario: d Explanation: The tub is being filled, which implies that the amount of water in the tub is increasing, so the line has a positive slope. Based on the graph, the amount of water is also increasing at a faster rate than in choice (a). CFU

M 6: LSN 4 Increasing and Decreasing Functions Exercise 1 - Continued Scenario: a Explanation: The bathtub is being filled, so the amount of water is increasing. This implies that the slope should be positive; however, the rate at which the tub is being filled is less than the rate for choice (d) CFU

Learning Objective Today, we will describe the functional relationship between two types of quantities by analyzing a graph. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development – Exercise 2 a The delivery charge remains constant regardless of the distance to destination. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development – Exercise 2 b Read through each of the scenarios, and sketch a graph of a function that models the situation. The initial value is �� 4. psi. �� The function increases at a rate of �� 4. psi for �� every �� 0 meters, or ��. psi�� 7 per meter. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development - Whiteboard Read through each of the scenarios, and sketch a graph of a function that models the situation. The initial value of the function is �� 00. The function is decreasing by �� 0 miles for �� 0 mph increase in speed. In other words, the function decreases by �� miles for every �� mph increase in speed. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development Match each part of the graph (A, B, and C) to its verbal description. Explain the reasoning behind your choice CFU

Increasing and Decreasing Functions M 6: LSN 4 Concept Development. Half of the factory workers went on strike, and not enough smartphones were produced for normal shipments. C; if half of the workers went on strike, then the number of smartphones produced would be less than normal. The rate of change for C is less than the rate of change for A CFU

Increasing and Decreasing Functions M 6: LSN 4 Concept Development. The production schedule was normal, and smartphones were shipped to the retail store at a constant rate. A; if the production schedule is normal, the rate of change of interval A is greater than the rate of change of interval C. CFU

Increasing and Decreasing Functions M 6: LSN 4 Concept Development. A defective electronic chip was found, and the factory had to shut down; so, no smartphones were shipped. B; if no smartphones are shipped to the store, the total number remains constant during that time CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development The relationship between Jameson’s account balance and time is modeled by the graph below. Write a story that models the situation represented by the graph. When is the function represented by the graph increasing? How does this relate to your story? When is the function represented by the graph decreasing? How does this relate to your story? CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development – Possible Answers Write a story that models the situation represented by the graph. Jameson was sick and did not work for almost a whole week. Then, he mowed several lawns over the next few days and deposited the money into his account after each job. It rained several days, so instead of working, Jameson withdrew money from his account each day to go to the movies and out to lunch with friends. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development – Possible Answers When is the function represented by the graph increasing? How does this relate to your story? Between �� and �� days. Jameson earned money mowing lawns and made a deposit to his account each day. The money earned for each day was constant for these days. This is represented by a straight line. CFU

M 6: LSN 4 Increasing and Decreasing Functions Concept Development – Possible Answers When is the function represented by the graph decreasing? How does this relate to your story? Between �� and �� 4 days. Since days ��–�� 4 are represented by a straight line, this means that Jameson spent the money constantly over these days. Jameson cannot work because it is raining. Perhaps he withdraws money from his account to spend on different activities each day because he cannot work. CFU

Closure 1. What did we learn today? 2. Why is this important to you? 3. How can you tell when a function is increasing or decreasing?