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5 4 --3- 2 -1

5 4 --3- 2 -1

Calculus: Early Transcendentals
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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### Function Graph and Table Explanation #### Graph Description The graph of \( y = f(x) \) is presented, showcasing the behavior of the function over a specified range of \( x \)-values. Key points and features include: - The graph begins at approximately \( x = -5 \) with an increasing slope and peaks around \( y = 5 \) just before \( x = -4 \). - It then decreases, reaching a local minimum at around \( x = -1 \) with \( y = 0 \). - The graph increases again, peaking at \( x = 2 \) with \( y = 3 \) before declining towards \( x = 4 \). #### Table Explanation A table is provided to illustrate values of another continuous function \( g(x) \), which complements the graph: \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline g(x) & 1 & 3 & -4 & 0 & 2 & 4 & 6 & 0 & -3 \\ \hline \end{array} \] - This table lists specific values of \( g(x) \) for \( x \) ranging from \(-4\) to \(4\). - For instance, at \( x = -3 \), \( g(x) = 3 \), while at \( x = 2 \), \( g(x) = 6 \). This combined visualization and tabulated data provide a comprehensive view of the function’s behavior, demonstrating specific values and trends that are critical for understanding its dynamics.
Transcribed Image Text:### Function Graph and Table Explanation #### Graph Description The graph of \( y = f(x) \) is presented, showcasing the behavior of the function over a specified range of \( x \)-values. Key points and features include: - The graph begins at approximately \( x = -5 \) with an increasing slope and peaks around \( y = 5 \) just before \( x = -4 \). - It then decreases, reaching a local minimum at around \( x = -1 \) with \( y = 0 \). - The graph increases again, peaking at \( x = 2 \) with \( y = 3 \) before declining towards \( x = 4 \). #### Table Explanation A table is provided to illustrate values of another continuous function \( g(x) \), which complements the graph: \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline g(x) & 1 & 3 & -4 & 0 & 2 & 4 & 6 & 0 & -3 \\ \hline \end{array} \] - This table lists specific values of \( g(x) \) for \( x \) ranging from \(-4\) to \(4\). - For instance, at \( x = -3 \), \( g(x) = 3 \), while at \( x = 2 \), \( g(x) = 6 \). This combined visualization and tabulated data provide a comprehensive view of the function’s behavior, demonstrating specific values and trends that are critical for understanding its dynamics.
**Mathematical Composition Exercise** 1. **Compute the exact value of** \( (f \circ g)(0) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box] 2. **Compute the exact value of** \( (g \circ f)(-1) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box] 3. **Compute the exact value of** \( (f \circ f)(2) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box]
Transcribed Image Text:**Mathematical Composition Exercise** 1. **Compute the exact value of** \( (f \circ g)(0) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box] 2. **Compute the exact value of** \( (g \circ f)(-1) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box] 3. **Compute the exact value of** \( (f \circ f)(2) \) *Enter the exact value or enter DNE if it is undefined.* [Input Box]
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