Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve and graph function f
![On this educational page, we present a piecewise function \( f(x) \), which is defined differently depending on the value of \( x \). Below is the detailed expression for the function:
\[
f(x) = \begin{cases}
\sqrt{-x} + 1 & \text{if } x \leq 0; \\
2 - x & \text{if } 0 < x \leq 2; \\
(x-2)^2 & \text{if } x > 2.
\end{cases}
\]
1. **For \( x \leq 0 \):**
- The function is defined as \( f(x) = \sqrt{-x} + 1 \).
2. **For \( 0 < x \leq 2 \):**
- The function is defined as \( f(x) = 2 - x \).
3. **For \( x > 2 \):**
- The function is defined as \( f(x) = (x - 2)^2 \).
Understanding piecewise functions is crucial as they can model situations where different rules apply to different parts of the domain. In this particular example, the function \( f(x) \) changes its definition based on the value of \( x \), providing a versatile tool for representing real-world scenarios in mathematical terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff91ef73-4530-48ba-be88-fd15c629792d%2F034cf679-7071-4a45-9ff1-c1fba7c91874%2Fcxt99pk_processed.png&w=3840&q=75)
Transcribed Image Text:On this educational page, we present a piecewise function \( f(x) \), which is defined differently depending on the value of \( x \). Below is the detailed expression for the function:
\[
f(x) = \begin{cases}
\sqrt{-x} + 1 & \text{if } x \leq 0; \\
2 - x & \text{if } 0 < x \leq 2; \\
(x-2)^2 & \text{if } x > 2.
\end{cases}
\]
1. **For \( x \leq 0 \):**
- The function is defined as \( f(x) = \sqrt{-x} + 1 \).
2. **For \( 0 < x \leq 2 \):**
- The function is defined as \( f(x) = 2 - x \).
3. **For \( x > 2 \):**
- The function is defined as \( f(x) = (x - 2)^2 \).
Understanding piecewise functions is crucial as they can model situations where different rules apply to different parts of the domain. In this particular example, the function \( f(x) \) changes its definition based on the value of \( x \), providing a versatile tool for representing real-world scenarios in mathematical terms.
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