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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Question
![**Function Analysis:**
Given the function:
\[ f(x) = x^3 - 5x^2 + 7x - 13 \]
**Domain:**
The domain of a polynomial function is all real numbers. Therefore, the domain of \( f(x) \) is:
\[ \text{Domain: } (-\infty, \infty) \]
**Range:**
The range of a cubic polynomial is also all real numbers, as it can take any real value. Therefore, the range of \( f(x) \) is:
\[ \text{Range: } (-\infty, \infty) \]
**Explanation:**
Polynomial functions are smooth and continuous over all real numbers, and both domain and range consist of all real values for this cubic function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90a41449-02d5-4122-bc31-788a957a2bcf%2Fac578b96-3551-4582-8399-06301db1fa1a%2F501gca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Function Analysis:**
Given the function:
\[ f(x) = x^3 - 5x^2 + 7x - 13 \]
**Domain:**
The domain of a polynomial function is all real numbers. Therefore, the domain of \( f(x) \) is:
\[ \text{Domain: } (-\infty, \infty) \]
**Range:**
The range of a cubic polynomial is also all real numbers, as it can take any real value. Therefore, the range of \( f(x) \) is:
\[ \text{Range: } (-\infty, \infty) \]
**Explanation:**
Polynomial functions are smooth and continuous over all real numbers, and both domain and range consist of all real values for this cubic function.
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