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
Justify that ...is continuous at x = 3.
![The image presents a mathematical function definition with a piecewise structure:
"Justify that
\[
f(x) =
\begin{cases}
\frac{x^2 - 2x - 3}{x - 3} & \text{if } x \neq 3, \\
4 & \text{if } x = 3
\end{cases}
\]
"
Here's an explanation of the function:
- The function \( f(x) \) is defined differently at \( x = 3 \) and at other values of \( x \).
- For \( x \neq 3 \), the function is expressed as a rational expression: \( \frac{x^2 - 2x - 3}{x - 3} \).
- For \( x = 3 \), the function has a value of 4.
This requires justification, likely involving demonstrating the function's continuity or finding a limit at \( x = 3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe03998fa-530b-45e4-aecb-4c80b62eaf29%2F4fc116db-02d0-4c80-9dc5-1a91e3408928%2Fctepj9a_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical function definition with a piecewise structure:
"Justify that
\[
f(x) =
\begin{cases}
\frac{x^2 - 2x - 3}{x - 3} & \text{if } x \neq 3, \\
4 & \text{if } x = 3
\end{cases}
\]
"
Here's an explanation of the function:
- The function \( f(x) \) is defined differently at \( x = 3 \) and at other values of \( x \).
- For \( x \neq 3 \), the function is expressed as a rational expression: \( \frac{x^2 - 2x - 3}{x - 3} \).
- For \( x = 3 \), the function has a value of 4.
This requires justification, likely involving demonstrating the function's continuity or finding a limit at \( x = 3 \).
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