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-5 -4 -3 -2 5 4 3 2 -1 -1 1 2 4

-5 -4 -3 -2 5 4 3 2 -1 -1 1 2 4

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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The graph presented is a continuous piecewise curve exhibiting varying slopes and points of interest, plotted on a Cartesian coordinate grid. Let's break it down: ### Graph Details - **Axes:** - The horizontal axis (x-axis) ranges approximately from -5 to 4. - The vertical axis (y-axis) ranges from -1 to 5. - **Key Points:** - The graph starts at approximately (-5, 2) with an upward slope. - A marked open circle is located at (-4, 4), indicating a point that the curve approaches but does not include. - The curve descends to a closed circle at (-3, 0), indicating a precise point included in the graph. - Continuing, the curve reaches its lowest point at (0, -1) with another open circle. - **Further Path:** - The curve rises to meet another marked point at (1, 2) with a closed circle, indicating inclusion. - Moving on, it peaks again at (2, 3) with a closed circle. - The graph then slopes downwards and ends at (4, 1) with an open circle, suggesting the curve approaches but does not include this point. ### Analysis - **Intervals and Slopes:** - From (-5, 2) to (-4, 4), the graph slopes upwards. - Decline begins sharply from (-4, 4) through (-3, 0) down to a trough at (0, -1). - The ascent from (0, -1) to (2, 3) showcases a smooth recovery. - The final decline occurs from (2, 3) to (4, 1). - **Open and Closed Circles:** - **Open circles**: (-4, 4), (0, -1), (4, 1) suggest that the endpoint is not part of the graph. - **Closed circles**: (-3, 0), (1, 2), (2, 3) indicate specific points that are included. ### Educational Insights This graph illustrates how functions can have segments with varying behaviors and discontinuities. Understanding open and closed intervals is vital in interpreting such piecewise functions, essential for students engaging with calculus and advanced algebra studies.
Transcribed Image Text:The graph presented is a continuous piecewise curve exhibiting varying slopes and points of interest, plotted on a Cartesian coordinate grid. Let's break it down: ### Graph Details - **Axes:** - The horizontal axis (x-axis) ranges approximately from -5 to 4. - The vertical axis (y-axis) ranges from -1 to 5. - **Key Points:** - The graph starts at approximately (-5, 2) with an upward slope. - A marked open circle is located at (-4, 4), indicating a point that the curve approaches but does not include. - The curve descends to a closed circle at (-3, 0), indicating a precise point included in the graph. - Continuing, the curve reaches its lowest point at (0, -1) with another open circle. - **Further Path:** - The curve rises to meet another marked point at (1, 2) with a closed circle, indicating inclusion. - Moving on, it peaks again at (2, 3) with a closed circle. - The graph then slopes downwards and ends at (4, 1) with an open circle, suggesting the curve approaches but does not include this point. ### Analysis - **Intervals and Slopes:** - From (-5, 2) to (-4, 4), the graph slopes upwards. - Decline begins sharply from (-4, 4) through (-3, 0) down to a trough at (0, -1). - The ascent from (0, -1) to (2, 3) showcases a smooth recovery. - The final decline occurs from (2, 3) to (4, 1). - **Open and Closed Circles:** - **Open circles**: (-4, 4), (0, -1), (4, 1) suggest that the endpoint is not part of the graph. - **Closed circles**: (-3, 0), (1, 2), (2, 3) indicate specific points that are included. ### Educational Insights This graph illustrates how functions can have segments with varying behaviors and discontinuities. Understanding open and closed intervals is vital in interpreting such piecewise functions, essential for students engaging with calculus and advanced algebra studies.
**Problem Statement:** From the list below, select the values of \( x \) for which \( f'(x) > 0 \). **Options:** - [ ] \( 2 \) - [ ] \(-1 \) - [ ] None of the listed \( x \) values - [ ] \(-3 \) - [ ] \(-2 \) - [ ] \( 3 \) - [ ] \( 1 \) - [ ] \( 0 \) - [ ] \(-4 \) **Explanation:** Select the box next to the values that meet the criteria of the derivative \( f'(x) \) being greater than zero at those points.
Transcribed Image Text:**Problem Statement:** From the list below, select the values of \( x \) for which \( f'(x) > 0 \). **Options:** - [ ] \( 2 \) - [ ] \(-1 \) - [ ] None of the listed \( x \) values - [ ] \(-3 \) - [ ] \(-2 \) - [ ] \( 3 \) - [ ] \( 1 \) - [ ] \( 0 \) - [ ] \(-4 \) **Explanation:** Select the box next to the values that meet the criteria of the derivative \( f'(x) \) being greater than zero at those points.
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