7) Give an example of an equation for a single function whose domain contains 2, whose domain does not contain 1, and whose range contains 0 but does not contain -1.

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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**Problem 7: Domain and Range of a Function**

*Question:*
Give an example of an equation for a single function whose domain contains 2, whose domain does not contain 1, and whose range contains 0 but does not contain -1.

*Explanation:*
This problem is asking for an example of a mathematical function that meets three specific criteria regarding its domain and range.

1. The function’s domain must include the number 2.
2. The function’s domain must exclude the number 1.
3. The function’s range must include the number 0.
4. The function’s range must exclude the number -1.

An educational example might involve the creation of a piecewise function or the use of a rational function with specific restrictions. For instance, the function could be designed in such a way that it is undefined at \( x = 1 \) and never reaches the value of -1.

If this question accompanies other graphical details or additional textual explanations, refer to those materials to understand how the function can be graphically represented and how the domain and range are determined.
Transcribed Image Text:**Problem 7: Domain and Range of a Function** *Question:* Give an example of an equation for a single function whose domain contains 2, whose domain does not contain 1, and whose range contains 0 but does not contain -1. *Explanation:* This problem is asking for an example of a mathematical function that meets three specific criteria regarding its domain and range. 1. The function’s domain must include the number 2. 2. The function’s domain must exclude the number 1. 3. The function’s range must include the number 0. 4. The function’s range must exclude the number -1. An educational example might involve the creation of a piecewise function or the use of a rational function with specific restrictions. For instance, the function could be designed in such a way that it is undefined at \( x = 1 \) and never reaches the value of -1. If this question accompanies other graphical details or additional textual explanations, refer to those materials to understand how the function can be graphically represented and how the domain and range are determined.
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