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**Title:** Sketching the Graph of a Polynomial Using a Sign Diagram **Introduction:** In this section, we will learn how to sketch the graph of a polynomial based on its sign diagram. **Sign Diagram Explanation:** The sign diagram provided represents the sign of the function \( f(x) \) over different intervals on the x-axis: - \( x < -4 \): The interval where \( f(x) \) is positive (+). - \( x = -4 \): A point where \( f(x) \) is equal to zero (0). - \(-4 < x < 0 \): The interval where \( f(x) \) is negative (−). - \( x = 0 \): A point where \( f(x) \) is equal to zero (0). - \( 0 < x < 3 \): The interval where \( f(x) \) is positive (+). - \( x = 3 \): A point where \( f(x) \) is equal to zero (0). - \( x > 3 \): A point where \( f(x) \) is zero (=). **Objective:** Use this sign information to help sketch the polynomial graph, identifying intervals of positivity/negativity and the roots of the polynomial where the graph intercepts the x-axis.

**Title:** Sketching the Graph of a Polynomial Using a Sign Diagram **Introduction:** In this section, we will learn how to sketch the graph of a polynomial based on its sign diagram. **Sign Diagram Explanation:** The sign diagram provided represents the sign of the function \( f(x) \) over different intervals on the x-axis: - \( x < -4 \): The interval where \( f(x) \) is positive (+). - \( x = -4 \): A point where \( f(x) \) is equal to zero (0). - \(-4 < x < 0 \): The interval where \( f(x) \) is negative (−). - \( x = 0 \): A point where \( f(x) \) is equal to zero (0). - \( 0 < x < 3 \): The interval where \( f(x) \) is positive (+). - \( x = 3 \): A point where \( f(x) \) is equal to zero (0). - \( x > 3 \): A point where \( f(x) \) is zero (=). **Objective:** Use this sign information to help sketch the polynomial graph, identifying intervals of positivity/negativity and the roots of the polynomial where the graph intercepts the x-axis.

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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**Title:** Sketching the Graph of a Polynomial Using a Sign Diagram **Introduction:** In this section, we will learn how to sketch the graph of a polynomial based on its sign diagram. **Sign Diagram Explanation:** The sign diagram provided represents the sign of the function \( f(x) \) over different intervals on the x-axis: - \( x < -4 \): The interval where \( f(x) \) is positive (+). - \( x = -4 \): A point where \( f(x) \) is equal to zero (0). - \(-4 < x < 0 \): The interval where \( f(x) \) is negative (−). - \( x = 0 \): A point where \( f(x) \) is equal to zero (0). - \( 0 < x < 3 \): The interval where \( f(x) \) is positive (+). - \( x = 3 \): A point where \( f(x) \) is equal to zero (0). - \( x > 3 \): A point where \( f(x) \) is zero (=). **Objective:** Use this sign information to help sketch the polynomial graph, identifying intervals of positivity/negativity and the roots of the polynomial where the graph intercepts the x-axis.
Transcribed Image Text:**Title:** Sketching the Graph of a Polynomial Using a Sign Diagram **Introduction:** In this section, we will learn how to sketch the graph of a polynomial based on its sign diagram. **Sign Diagram Explanation:** The sign diagram provided represents the sign of the function \( f(x) \) over different intervals on the x-axis: - \( x < -4 \): The interval where \( f(x) \) is positive (+). - \( x = -4 \): A point where \( f(x) \) is equal to zero (0). - \(-4 < x < 0 \): The interval where \( f(x) \) is negative (−). - \( x = 0 \): A point where \( f(x) \) is equal to zero (0). - \( 0 < x < 3 \): The interval where \( f(x) \) is positive (+). - \( x = 3 \): A point where \( f(x) \) is equal to zero (0). - \( x > 3 \): A point where \( f(x) \) is zero (=). **Objective:** Use this sign information to help sketch the polynomial graph, identifying intervals of positivity/negativity and the roots of the polynomial where the graph intercepts the x-axis.
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