/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 123 What is a piecewise function?... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 123

What is a piecewise function?

Short Answer

Expert verified
A piecewise function is a function with different formulas for different input intervals. It consists of multiple 'piece' functions each defined on specific domains. To solve it, determine the appropriate 'piece' for the given input and evaluate.

Step by step solution

01

Understand and Define a Piecewise Function

A Piecewise function is a type of function that allows differing function formulas for differing input values. For different ranges of input values, different functions can be applied. Thus, it is a function whose definition changes depending on the value of the input. It's usually represented as \( f(x) = \begin{cases} f_1(x) & \text{for } x \in D_1 \ f_2(x) & \text{for } x \in D_2 \ \vdots & \vdots \ f_n(x) & \text{for } x \in D_n \end{cases} \) where each \(f_i(x)\) is a function for the domain \(D_i\).
02

Interpret the Piecewise Function

To interpret a piecewise function, you need to identify the intervals of the input variable where each of the 'piece' functions apply. You may need to graph the pieces individually to fully understand how the function behaves across its entire domain.
03

Evaluate or Solve the Piecewise Function

To solve or evaluate a piecewise function, identify in which interval the input value falls and substitute it in the corresponding function.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by A mericans \(x\) years after \(1950 .\) (GRAPH CAN'T COPY) In \(1950,\) Americans spent \(22 \%\) of their budget on food. This has decreased at an average rate of approximately \(0.25 \%\) per year since then.

You have 800 feet of fencing to enclose a rectangular field. Express the area of the field, \(A\), as a function of one of its dimensions, \(x\).

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by A mericans \(x\) years after \(1950 .\) (GRAPH CAN'T COPY) In \(1950,\) Americans spent \(3 \%\) of their budget on health care. This has increased at an average rate of approximately \(0.22 \%\) per year since then.

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. \(x\) -intercept \(=-\frac{1}{2}\) and \(y\) -intercept \(=4\)

The annual yield per lemon tree is fairly constant at 320 pounds per tree when the number of trees per acre is 50 or fewer. For each additional tree over \(50,\) the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. a. Express the yield per tree, \(Y\), in pounds, as a function of the number of lemon trees per acre, \(x\). b. Express the total yield for an acre, \(T\), in pounds, as a function of the number of lemon trees per acre, \(x\).
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.