Common Core Algebra Unit 16 Extension: Other Types of Functions 5/15/17Lesson 3 Extension: Step FunctionsObjective: SWBAT identify, write, and graph step functions.Do Now:Consider the piecewise (step) function given by

Step FunctionsA step function is a piecewise function containing all horizontal "pieces". A step function

resembles a set of steps and is discontinuous (cannot be drawn without removing your pencil from the paper).

Model Example:A step function is defined using the piecewise formula.

Check for Understanding:Which graph represents the function below?

a. b. c. d.

Explain how you arrived at your answer:

Turn and Talk:Let’s take a look at these functions in the context of a situation.

The graph shows the rates for parking in a city-parking garage.

A) How much does it cost to park for 30 minutes?

B) How much will it cost if someone is planning to park for 4 hours?

C) If a person pays $15 for parking, how many hours has he/she parked?

D) Create a sign for the parking rates based on this graph below.

Model Example:At a local amusement park, the park charges an admission based on age. Graph the amount of money a person would have to pay for admission based on their age. Remember that someone who is one day short of 4 years old can consider themselves three and under.

Check for Understanding:The table below lists the total cost for parking for a period of time on a street in Albany, N.Y. The total cost is for any length of time up to and including the hours parked. For example, parking for up to and including 1 hour would cost $1.25; parking for 3.5 hours would cost $5.75.

Graph the step function that represents the cost for the number of hours parked.

Explain how the cost per hour to park changes over the six-hour period

Take Away:

A step function is a piecewise function containing all ________________"pieces". A step function resembles a

set of steps and is __________________ (cannot be drawn without removing your pencil from the paper).

Partner Practice:

1.

2.

3. Erin buys gas at a self-service station for $2.75 a gallon. The gas station has a promotion going on that anyone who buys more than 10 gallons of gas, only has to pay $2.50 per gallon. Erin’s tank will hold 12 gallons of gas.a) Write a rule for the total cost, C(g), as a function of g gallons of gas.

b) Graph the piecewise function.

c) What is the domain and range of the function?

4. An electrician works at a job site at a rate of $40 per hour or any portion of an hour. In other words, he will charge you $40 as soon as he comes up to the first hour, and then $40 for the second hour, etcetera.

a) Graph the amount the electrician charges, c, in dollars as a function of the number of hours he works.

b) How much does he charge for working 3.5 hours? Circle the point on the graph the shows this answer.

5. A pumping station is draining a reservoir with a set of pumps that drain the water at a rate of 250 gallons per hour. After 5 hours, additional pumps are turning on such that they pump at an overall rate of 600 gallons per hour for the next 7 hours.(a) Draw a graph of the pump rate function on the grid provided.

b) How many total gallons of water are pumped out of the reservoir over the 12 hour period? Show the calculations that lead to your answer.

c) The reservoir originally contains 8,250 gallons of water. How much does it contain after 5 hours if water is only pumped out? Explain your answer in sentences.

d) Engineers want to turn off the pumps when the reservoir reaches a level of 2,000 gallons. Will they need to turn the pumps off during this 12-hour time period? Show evidence to support your yes/no answer.

e) Assuming engineers do not turn off any pumps, how many total hours will it take, to the nearest tenth of an hour, to drain the reservoir of all of its water?

5. When kimchi is made, it is initially fermented for the first 3 days at a temperature of 70 degrees Fahrenheitand then immediately moved to a temperature of 50 degrees Fahrenheit for another 3 days after which it isput in a 35 degree refrigerator for 6 days.

6.

Name ___________________________ Exit Slip

Common Core Algebra Unit 16 Extension: Other Types of Functions 5/15/17Lesson 3 Extension: Step FunctionsObjective: SWBAT identify, write, and graph step functions.

Morgan can start wrestling at age 5 in Division 1. He remains in that division until his next odd birthday when

he is required to move up to the next division level. Which graph correctly represents this information?

1. 2. 3. 4.

Name ___________________________ Exit Slip

Common Core Algebra Unit 16 Extension: Other Types of Functions 5/15/17Lesson 3 Extension: Step FunctionsObjective: SWBAT identify, write, and graph step functions.

Morgan can start wrestling at age 5 in Division 1. He remains in that division until his next odd birthday when

he is required to move up to the next division level. Which graph correctly represents this information?

1. 2. 3. 4.