APPLICATIONS TO LINEAR PIECEWISEDEFINED FUNCTIONS UNIT 1 FIF

APPLICATIONS TO LINEAR PIECEWISE-DEFINED FUNCTIONS UNIT 1

F-IF. 4: I can create a function that models a relationship between two quantities, interpret key features of the graph and sketch graph showing key features. F-IF. 7. b: I can graph a piecewise defined function. https: //www. youtube. com/wat

ABSOLUTE VALUE PARENT FUNCTION Example of a piecewise function.

PIECEWISE FUNCTIONS are presented by a combination of equations, or pieces, each corresponding to different defined domains.

Today’s work will be completed on your desktop using a whiteboard marker.

GUIDED PRACTICE EXAMPLE 1 The weekday parking rates for a garage are shown to the right. Create a graph that models the cost weekday parking charges at this Garage Rates (Weekdays) $3 per half hour $8 maximum for 12 hours

1 3 5 Cost (dollars) 7 Garage Rates (Weekdays $3 per half hour $8 maximum for 12 hour Time (hours)

1 3 5 Cost (dollars) 7 Garage Rates (Weekdays $3 per half hour $8 maximum for 12 hours Time (hours)

ANALYZING THE GRAPH How much would it cost you to park in this parking garage for six hours?

ANALYZING THE GRAPH How much would it cost you to park in this parking garage for six hours? It would cost $8 to park in the garage for six hours.

ANALYZING THE GRAPH How much would it cost you to park in this parking garage forty-five minutes?

ANALYZING THE GRAPH How much would it cost you to park in this parking garage forty-five minutes? It would cost $6 to park in the garage forty-five minutes.

ANALYZING THE GRAPH How much would it cost you to park in this parking garage for one hour?

ANALYZING THE GRAPH How much would it cost you to park in this parking garage for one hour? It would cost $6 to park in the garage for one hour.

ANALYZING THE GRAPH Identify the domain for the piecewise in interval notation defined by the function.

ANALYZING THE GRAPH Identify the domain for the piecewise in interval notation defined by the function. 0 < t < 12 (0, 12]

ANALYZING THE GRAPH Identify the range for the piecewise defined by the function.

ANALYZING THE GRAPH Identify the range for the piecewise defined by the function. {3, 6, 8}

ANALYZING THE GRAPH This piecewise defined function consists of how many equations or pieces? Write an equation for each portion of the piecewise function, and then define its domain.

ANALYZING THE GRAPH This piecewise defined function consists of how many equations or pieces? The piecewise defined function consists of three unique equations or pieces. Write an equation for each portion of the piecewise function, and then define its domain. y=3 0 < t < 0. 5 y=6 0. 5 < t < 1 y=8

ANALYZING THE GRAPH Write a complete piecewise defined function for the parking charges in this problem. Predict how the graph would change if the garage rate was $18 maximum for 12 hours.

ANALYZING THE GRAPH Write a complete piecewise defined function for the parking charges in this problem. Turn to your partner and predict how the graph would change if the garage rate was $18 maximum for 12 hours.

Erase your desk.

INDEPENDENT PRACTICE EXAMPLE 2 Karen has a summer job as a lifeguard at a local swimming pool. The pool is open from 5 am -11 am and 1 pm – 5 pm seven days a week. Her job that pays time and a half for overtime. That is, if she works more than 40 hours per week, her hourly wage for the extra hours is 1. 5 times her normal hourly wage of $8. Create a graph that models the how much Karen can make at her summer job in

400 200 50 Pay (dollars) Graph the function for this scenario. Hour Worked at the Pool

400 200 50 Paycheck (dollars) Graph the function for this scenario. Hour Worked at the Pool

ANALYZING THE GRAPH If Karen gets paid weekly, how much can she expect to earn if she works 30 hours in one week? If Karen gets paid weekly, how much can she expect to earn if she works 40 hours in one week? If Karen gets paid weekly, how much can she expect to earn if she works 55 hours in one week?

ANALYZING THE GRAPH Using interval notation define the domain for this piecewise defined function. Using interval notation define the range for this piecewise defined function. Why is it reasonable to assume that the domain and range have limitations?

ANALYZING THE GRAPH Why is it reasonable to assume that the domain and range have limitations?

ANALYZING THE GRAPH This piecewise defined function consists of how many comprised equations? Write an equation for each portion of the piecewise function, and then define its domain.

Hour Worked at the Pool 50 200 400 Paycheck (dollars)

ANALYZING THE GRAPH Write a complete piecewise defined function for the parking charges in this problem. Predict how much Karen will get paid if she works 45 hours in one week.

ANALYZING THE GRAPH Write a complete piecewise defined function for the parking charges in this problem. Predict how much Karen will get paid if she works 45 hours in one week.

CONCEPT CHECKS Define a piecewise function. Give an example. What does a solid dot on the graph of a piecewise function indicate? What does an open dot indicate?

Do the graphs below satisfy the condition for being a function? Explain. Example 1 Example 2 Example 3

INDEPENDENT PRACTICE EXAMPLE 3 What piecewise function represents the graph to the right?

INDEPENDENT PRACTICE EXAMPLE 4 What piecewise function represents the graph to the right?