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Give the domain and range. Then, use the graph to find (a) f( − 2), (b) f(0), (c) (1) and (d) any values of x such that f(x) = 4. 10- 4 3 L

Give the domain and range. Then, use the graph to find (a) f( − 2), (b) f(0), (c) (1) and (d) any values of x such that f(x) = 4. 10- 4 3 L

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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**Domain and Range Analysis with Graph Interpretation** **Introduction:** In this lesson, we will analyze the given graph to determine its domain and range. Additionally, we will use the graph to find specific function values and identify any x-values for which the function equals 4. **Domain and Range:** The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values) the function can take. **Graph Explanation:** The graph provided is a piecewise linear function depicted in a coordinate plane. The x-axis represents the input variable \(x\), and the y-axis represents the output variable \(y\). The graph has distinct line segments connecting several key points. Key Points on the Graph: - (-2, 0) - (0, 8) - (2, 0) - (2, 10) **Detailed Questions:** (a) **Find \( f(-2) \):** Locate x = -2 on the x-axis and find the corresponding y-value on the graph. \( f(-2) = 0 \). (b) **Find \( f(0) \):** Locate x = 0 on the x-axis and find the corresponding y-value on the graph. \( f(0) = 8 \). (c) **Find \( f\left(\frac{1}{2}\right) \):** Locate x = 0.5 (since \(\frac{1}{2}\) is equal to 0.5) on the x-axis and find the corresponding y-value on the graph. \( f(0.5) = 6 \). (d) **Any values of x such that \( f(x) = 4 \):** Find all x-values where the graph intersects the line y = 4. - From the graph, we can see that at \( x = -1 \) and \( x = 1.5 \), \( f(x) = 4 \). *Graphical Representation Explanation:* - The x-axis ranges from -2 to 2. - The y-axis ranges from 0 to 10. - The function starts at point (-2, 0), rises to (0, 8), drops to (2, 0), and rises again to (2, 10). **Conclusion:** Analy
Transcribed Image Text:**Domain and Range Analysis with Graph Interpretation** **Introduction:** In this lesson, we will analyze the given graph to determine its domain and range. Additionally, we will use the graph to find specific function values and identify any x-values for which the function equals 4. **Domain and Range:** The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values) the function can take. **Graph Explanation:** The graph provided is a piecewise linear function depicted in a coordinate plane. The x-axis represents the input variable \(x\), and the y-axis represents the output variable \(y\). The graph has distinct line segments connecting several key points. Key Points on the Graph: - (-2, 0) - (0, 8) - (2, 0) - (2, 10) **Detailed Questions:** (a) **Find \( f(-2) \):** Locate x = -2 on the x-axis and find the corresponding y-value on the graph. \( f(-2) = 0 \). (b) **Find \( f(0) \):** Locate x = 0 on the x-axis and find the corresponding y-value on the graph. \( f(0) = 8 \). (c) **Find \( f\left(\frac{1}{2}\right) \):** Locate x = 0.5 (since \(\frac{1}{2}\) is equal to 0.5) on the x-axis and find the corresponding y-value on the graph. \( f(0.5) = 6 \). (d) **Any values of x such that \( f(x) = 4 \):** Find all x-values where the graph intersects the line y = 4. - From the graph, we can see that at \( x = -1 \) and \( x = 1.5 \), \( f(x) = 4 \). *Graphical Representation Explanation:* - The x-axis ranges from -2 to 2. - The y-axis ranges from 0 to 10. - The function starts at point (-2, 0), rises to (0, 8), drops to (2, 0), and rises again to (2, 10). **Conclusion:** Analy
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