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
![### Graph of the Function \( f(x) \)
The graph provided represents the function \( f(x) \). Answer the questions below regarding the behavior of \( f(x) \) as \( x \) approaches 2 and the value of \( f(2) \).
#### Graph Description
The graph is drawn on a Cartesian coordinate plane with the y-axis and x-axis clearly marked. The x-axis ranges from -10 to 10, and the y-axis ranges from -8 to 8.
#### Key Points on the Graph
- The function \( f(x) \) intersects the x-axis at several points and has various maxima and minima.
- Around \( x = 2 \), three points are specifically marked:
- The function approaches a value from the left of \( x = 2 \).
- The function is undefined at \( x = 2 \).
- The function approaches a different value from the right of \( x = 2 \).
- The open circle denotes a point where the function does not exist, indicating a discontinuity.
### Questions
Use the provided graph to answer the questions about the limits and the value of the function at \( x = 2 \).
1. \(\lim_{x \to 2^-} f(x) =\) [Answer]
2. \(\lim_{x \to 2^+} f(x) =\) [Answer]
3. \(\lim_{x \to 2} f(x) =\) [Answer]
4. \( f(2) =\) [Answer]
#### Options
- \( \infty \)
- 0
- \( DNE \) (Does Not Exist)
- undefined
Fill in the values accordingly based on the graph provided to answer the behavior of the function near \( x = 2 \).
---
The graph analysis will help understand the limits and the continuity of the function \( f(x) \). These concepts are fundamental in calculus, particularly in understanding how functions behave at specific points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F991e22e9-7073-4035-a9d1-c12914250c1e%2F0dd562b9-87cb-4578-9e1f-cf3d6960eb65%2Fkt0zoge_processed.png&w=3840&q=75)
Transcribed Image Text:### Graph of the Function \( f(x) \)
The graph provided represents the function \( f(x) \). Answer the questions below regarding the behavior of \( f(x) \) as \( x \) approaches 2 and the value of \( f(2) \).
#### Graph Description
The graph is drawn on a Cartesian coordinate plane with the y-axis and x-axis clearly marked. The x-axis ranges from -10 to 10, and the y-axis ranges from -8 to 8.
#### Key Points on the Graph
- The function \( f(x) \) intersects the x-axis at several points and has various maxima and minima.
- Around \( x = 2 \), three points are specifically marked:
- The function approaches a value from the left of \( x = 2 \).
- The function is undefined at \( x = 2 \).
- The function approaches a different value from the right of \( x = 2 \).
- The open circle denotes a point where the function does not exist, indicating a discontinuity.
### Questions
Use the provided graph to answer the questions about the limits and the value of the function at \( x = 2 \).
1. \(\lim_{x \to 2^-} f(x) =\) [Answer]
2. \(\lim_{x \to 2^+} f(x) =\) [Answer]
3. \(\lim_{x \to 2} f(x) =\) [Answer]
4. \( f(2) =\) [Answer]
#### Options
- \( \infty \)
- 0
- \( DNE \) (Does Not Exist)
- undefined
Fill in the values accordingly based on the graph provided to answer the behavior of the function near \( x = 2 \).
---
The graph analysis will help understand the limits and the continuity of the function \( f(x) \). These concepts are fundamental in calculus, particularly in understanding how functions behave at specific points.
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