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The graph of a function is given. y 2 X 1 (a) Determine the net change between the indicated points on the graph.

The graph of a function is given. y 2 X 1 (a) Determine the net change between the indicated points on the graph.

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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### Understanding the Graph of a Function The image shows a graph of a function plotted on a coordinate plane with x and y axes. The function's graph is represented by a red curve, which showcases multiple peaks and troughs, illustrating a non-linear relationship. #### Key Features of the Graph - **Axes**: - The horizontal axis is labeled as the *x-axis*. - The vertical axis is labeled as the *y-axis*. - **Curve Description**: - The red curve initially rises to a peak, falls to a trough, and rises again. - It starts below the x-axis to the left, peaks around the point (-0.5, 3), and moves to a trough near the point (2.5, 1) before rising sharply. - **Indicated Points**: - A point is marked through where the curve peaks at approximately (0, 3). - A second point is indicated on the red curve at the end, where the function rises again. - **Dashed Line**: - A dashed line runs diagonally from the peak around (0, 3) to the rising point on the right portion of the graph. This line may represent a linear approximation or path connecting significant points on the graph. #### Task (a) **Determine the net change between the indicated points on the graph.** To solve this, calculate the difference in the y-values between the indicated points on the red curve. This will give the vertical change, or net change, between these points. This graph serves to illustrate the dynamics of the function and can be used to analyze changes, behavior, and potential applications in an educational context.
Transcribed Image Text:### Understanding the Graph of a Function The image shows a graph of a function plotted on a coordinate plane with x and y axes. The function's graph is represented by a red curve, which showcases multiple peaks and troughs, illustrating a non-linear relationship. #### Key Features of the Graph - **Axes**: - The horizontal axis is labeled as the *x-axis*. - The vertical axis is labeled as the *y-axis*. - **Curve Description**: - The red curve initially rises to a peak, falls to a trough, and rises again. - It starts below the x-axis to the left, peaks around the point (-0.5, 3), and moves to a trough near the point (2.5, 1) before rising sharply. - **Indicated Points**: - A point is marked through where the curve peaks at approximately (0, 3). - A second point is indicated on the red curve at the end, where the function rises again. - **Dashed Line**: - A dashed line runs diagonally from the peak around (0, 3) to the rising point on the right portion of the graph. This line may represent a linear approximation or path connecting significant points on the graph. #### Task (a) **Determine the net change between the indicated points on the graph.** To solve this, calculate the difference in the y-values between the indicated points on the red curve. This will give the vertical change, or net change, between these points. This graph serves to illustrate the dynamics of the function and can be used to analyze changes, behavior, and potential applications in an educational context.
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