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What is the egualion of Hhe line over the intereval (5, ] ? What would the exact value of the x-intercept be if it existed? Polts gilen on grephi (5,-3) and (2,4)

What is the egualion of Hhe line over the intereval (5, ] ? What would the exact value of the x-intercept be if it existed? Polts gilen on grephi (5,-3) and (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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**Title: Determining the Equation of a Line and X-Intercept** **Problem Statement:** 1. **Question:** What is the equation of the line over the interval \([-5, 2]\)? 2. **Further Inquiry:** What would the exact value of the x-intercept be if it existed? **Given Data:** - Points on the graph: \((-5, -3)\) and \((-2, 4)\) **Approach:** To find the equation of the line, we need to determine the slope using the points provided and then identify the equation in slope-intercept form. Once we have the equation, we can calculate the x-intercept if it exists.
Transcribed Image Text:**Title: Determining the Equation of a Line and X-Intercept** **Problem Statement:** 1. **Question:** What is the equation of the line over the interval \([-5, 2]\)? 2. **Further Inquiry:** What would the exact value of the x-intercept be if it existed? **Given Data:** - Points on the graph: \((-5, -3)\) and \((-2, 4)\) **Approach:** To find the equation of the line, we need to determine the slope using the points provided and then identify the equation in slope-intercept form. Once we have the equation, we can calculate the x-intercept if it exists.
The image shows the "Graph of f(x)," which appears to be a piecewise function with several distinct sections and notable points. Below is a detailed explanation of the graph: 1. **Axes**: The graph is plotted on a Cartesian coordinate system with x and y-axes ranging approximately from -3 to 5 on both axes. 2. **Data Points and Sections**: - The graph starts in the negative x region, and initially moves upward reaching a peak. - The first peak is at the coordinates (0, 4). - The graph then descends sharply from this peak to around (1, 0). - It continues to descend slightly below the x-axis to a minimum point near (1.5, -3). - Following this, the curve rises again, creating a small secondary peak around (2.5, 0). - The graph dips once more, reaching another low point approximately at (3, -4). 3. **Overall Shape**: The graph has a sharp increase and decrease, resembling a wave pattern with varying amplitudes and frequencies. This visual representation of the function can be useful for understanding the behavior of the function f(x) over a range of x values and can illustrate concepts such as maxima, minima, and inflection points.
Transcribed Image Text:The image shows the "Graph of f(x)," which appears to be a piecewise function with several distinct sections and notable points. Below is a detailed explanation of the graph: 1. **Axes**: The graph is plotted on a Cartesian coordinate system with x and y-axes ranging approximately from -3 to 5 on both axes. 2. **Data Points and Sections**: - The graph starts in the negative x region, and initially moves upward reaching a peak. - The first peak is at the coordinates (0, 4). - The graph then descends sharply from this peak to around (1, 0). - It continues to descend slightly below the x-axis to a minimum point near (1.5, -3). - Following this, the curve rises again, creating a small secondary peak around (2.5, 0). - The graph dips once more, reaching another low point approximately at (3, -4). 3. **Overall Shape**: The graph has a sharp increase and decrease, resembling a wave pattern with varying amplitudes and frequencies. This visual representation of the function can be useful for understanding the behavior of the function f(x) over a range of x values and can illustrate concepts such as maxima, minima, and inflection points.
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