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Name Group Members Chapter 2 Concept Problem: Real World Piecewise Function Date Objective: To use a piecewise function to represent a real world situation. Tax Rate Schedule Problem In the United.

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One of the most common uses of piecewise functions comes from business and economics in the form of tax brackets. In the United States, taxes are paid to the U.S. government by citizens 18 years of age and older. Taxes pay for government programs like Medicare, public education, infrastructure, and much more.

A simple example of the need for piecewise functions occurs when you lease a car. To lease a car is to essentially rent the car for a period of time. You lease a car for four years for with a mile limit of miles. This limit means that if you drive more than miles, you will have to pay a fee.

Piecewise functions are defined by different functions throughout the different intervals of the domain. We actually apply piecewise functions in our lives more than we think so. Tax brackets, estimating our mobile phone plans, and even our salaries (with overtime pay) make use of piecewise functions.

Functions can be applied in various real-life situations to determine relationships between variables, such as calculating the cost of a product based on the quantity purchased or predicting the growth of a population over time.

For piecewise defined functions, we often have to be very careful in com- puting the derivatives. The differentiation rules (product, quotient, chain rules) can only be applied if the function is defined by ONE formula in a neighborhood of the point where we evaluate the derivative.

Generally, if you graph a piecewise function and at any point it doesn't look "smooth" (there's a "sharp" turn), then it is not differentiable at that point.

A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1.

Another example of a piecewise function is the absolute value function. The absolute value function can be written as f ( x ) = | x | . This function has three different pieces, x for all values less than 1, x 2 for all values between 1 and 3 (including 1 and 3) and finally, x + 3 for all values greater than three.

In a mathematical sense, these relationships can be referred to as one to one functions, in which there are equal numbers of items, or one item can only be paired with only one other item. The name of a person and the reserved seat number of that person in a train is a simple daily life example of one to one function.

Applications of Functions Finding how far someone travels after a certain amount of time. Predicting expected tree growth. Determining how much money to expect from investments. Calculating how much profit can be earned from sales.

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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
All Forms
Search all Forms
Industries
Forms in Spanish
Localized Forms
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232