☺ use the groph of the funchion f to the following limits.and funchion values

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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### Using the Graph of the Function \( f \) to Find Limits and Function Values

The image contains instructions and a graph of a function \( f \). The primary goal is to use the graph to determine specific limits and function values. Below are the details and graph interpretation for each query:

1. **Use the graph of the function \( f \) to find the following limits and function values.**

   **Graph Description:**
   - The graph is a sketch of the function \( f \) plotted on the \( xy \)-plane.
   - The \( x \)-axis ranges from slightly less than \(-1\) to slightly more than \( 4 \), while the \( y \)-axis ranges from slightly less than \( 1 \) to slightly more than \( 3 \).
   - Critical points on the graph:
     - At \( x = -1 \), the graph has a vertical asymptote.
     - The function has a value of \( f(0) = 3 \) at \( x = 0 \).
     - At \( x = 2 \), the graph passes through a hollow circle at \( y = 2 \), indicating a limit or a removable discontinuity.
     - At \( x = 4 \), the graph has a vertical asymptote, and \( f(4) \) is shown as a filled circle at \( y = 1 \).

   **Tasks and Points of Interest:**
   - \( a. \ f(-1) \)
   - \( b. \ \lim\limits_{x \to -1^+} f(x) \)
   - \( c. \ f(0) \)
   - \( d. \ \lim\limits_{x \to 0^-} f(x) \)
   - \( e. \ f(2) \)
   - \( f. \ \lim\limits_{x \to 2} f(x) \)
   - \( g. \ f(4) \)
   - \( h. \ \lim\limits_{x \to 4^-} f(x) \)

Using the information from the graph, students can determine the specific limits and function values as described by the function \( f \).
Transcribed Image Text:### Using the Graph of the Function \( f \) to Find Limits and Function Values The image contains instructions and a graph of a function \( f \). The primary goal is to use the graph to determine specific limits and function values. Below are the details and graph interpretation for each query: 1. **Use the graph of the function \( f \) to find the following limits and function values.** **Graph Description:** - The graph is a sketch of the function \( f \) plotted on the \( xy \)-plane. - The \( x \)-axis ranges from slightly less than \(-1\) to slightly more than \( 4 \), while the \( y \)-axis ranges from slightly less than \( 1 \) to slightly more than \( 3 \). - Critical points on the graph: - At \( x = -1 \), the graph has a vertical asymptote. - The function has a value of \( f(0) = 3 \) at \( x = 0 \). - At \( x = 2 \), the graph passes through a hollow circle at \( y = 2 \), indicating a limit or a removable discontinuity. - At \( x = 4 \), the graph has a vertical asymptote, and \( f(4) \) is shown as a filled circle at \( y = 1 \). **Tasks and Points of Interest:** - \( a. \ f(-1) \) - \( b. \ \lim\limits_{x \to -1^+} f(x) \) - \( c. \ f(0) \) - \( d. \ \lim\limits_{x \to 0^-} f(x) \) - \( e. \ f(2) \) - \( f. \ \lim\limits_{x \to 2} f(x) \) - \( g. \ f(4) \) - \( h. \ \lim\limits_{x \to 4^-} f(x) \) Using the information from the graph, students can determine the specific limits and function values as described by the function \( f \).
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