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or the given graphs, determine the intervals where the graph is increasing, decreasing, and/o onstant. 1.) -5 -10- -5- 0 -5. 5 tent.blackboardcdn.com/608c5b 10

or the given graphs, determine the intervals where the graph is increasing, decreasing, and/o onstant. 1.) -5 -10- -5- 0 -5. 5 tent.blackboardcdn.com/608c5b 10

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: Analyzing Intervals of a Graph** **Instructions:** For the given graph, determine the intervals where the graph is increasing, decreasing, and/or constant. **Graph Description:** 1. **Graph Overview:** The graph is plotted on a coordinate plane with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. The graph represents a polynomial function with a wavy curve exhibiting both increasing and decreasing behaviors. 2. **Analysis of the Graph:** - **Decreasing Intervals:** The graph decreases from the left side starting beyond x = -10 to approximately x = -3. - **Increasing Intervals:** From around x = -3 to x = 0, the graph increases. It decreases again from x = 0 to around x = 3. Beyond x = 3, the graph increases continuously towards the right. 3. **Important Points:** - **Turning Points:** There appears to be a local maximum around x = -3 and a local minimum near x = 0. Another turning point is observed around x = 3 where the graph shifts from decreasing to increasing. **Objective:** By examining these intervals, students can understand how functions behave over different x-values and identify key features like turning points and local extrema.
Transcribed Image Text:**Title: Analyzing Intervals of a Graph** **Instructions:** For the given graph, determine the intervals where the graph is increasing, decreasing, and/or constant. **Graph Description:** 1. **Graph Overview:** The graph is plotted on a coordinate plane with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. The graph represents a polynomial function with a wavy curve exhibiting both increasing and decreasing behaviors. 2. **Analysis of the Graph:** - **Decreasing Intervals:** The graph decreases from the left side starting beyond x = -10 to approximately x = -3. - **Increasing Intervals:** From around x = -3 to x = 0, the graph increases. It decreases again from x = 0 to around x = 3. Beyond x = 3, the graph increases continuously towards the right. 3. **Important Points:** - **Turning Points:** There appears to be a local maximum around x = -3 and a local minimum near x = 0. Another turning point is observed around x = 3 where the graph shifts from decreasing to increasing. **Objective:** By examining these intervals, students can understand how functions behave over different x-values and identify key features like turning points and local extrema.
The image presents a graph labeled "2.)" featuring a parabolic curve on a coordinate plane. ### Graph Description - **Axes:** - The x-axis ranges from -5 to 10. - The y-axis ranges from -5 to 15. - **Curve:** - The graph depicts a parabola opening upwards. - The vertex of the parabola is located near the point (0, 0). - As the curve extends, it intersects the y-axis above 10. This graph can illustrate a quadratic function, where its standard form might resemble \( y = ax^2 + bx + c \). Understanding the vertex and symmetry of the parabola is crucial for solving and graphing quadratic equations.
Transcribed Image Text:The image presents a graph labeled "2.)" featuring a parabolic curve on a coordinate plane. ### Graph Description - **Axes:** - The x-axis ranges from -5 to 10. - The y-axis ranges from -5 to 15. - **Curve:** - The graph depicts a parabola opening upwards. - The vertex of the parabola is located near the point (0, 0). - As the curve extends, it intersects the y-axis above 10. This graph can illustrate a quadratic function, where its standard form might resemble \( y = ax^2 + bx + c \). Understanding the vertex and symmetry of the parabola is crucial for solving and graphing quadratic equations.
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