12 ### Domain and Range Analysis**Objective:**To determine the domain and range of the given graph and use it to find specific values.**Graph Analysis:**The graph provided on the right shows a function plotted on a Cartesian plane with the x-axis and y-axis labeled from -6 to 6. The graph passes through several points within this coordinate range.**Domain and Range:**- The **domain** of the graph is the set of all possible \( x \)-values for which the graph is defined. - **Domain: \([-3, 5]\)** - The **range** of the graph is the set of all possible \( y \)-values that the graph can take. - **Range: \([-2, 2]\)****Tasks:**Use the graph to find the following function values:1. **Find \( f(-3) \)**: - From the graph, locate \( x = -3 \) and determine the corresponding \( y \)-value. - **\( f(-3) = -2 \)**2. **Find \( f(0) \)**: - From the graph, locate \( x = 0 \) and determine the corresponding \( y \)-value. - **\( f(0) = 1 \)**3. **Find \( f\left(\frac{1}{2}\right) \)**: - From the graph, locate \( x = \frac{1}{2} \) and determine the corresponding \( y \)-value. - **\( f\left(\frac{1}{2}\right) = \) [Value needs to be determined from the given graph]****Graph Explanation:**- The graph is a curve that traverses through different quadrants.- The specified domain \([-3,5]\) means that the graph starts from \( x = -3 \) and ends at \( x = 5 \).- The specified range \([-2,2]\) indicates that the \( y \)-values of the graph range from \(-2\) to \(2\).By analyzing the graph accordingly, one can determine the exact values for various function inputs as requested. ### Linear Graph RepresentationIn this educational module, we will explore the linear graph depicted above. A graph is a visual representation of data and functions that provide insights into trends and relationships between variables.#### Graph AnalysisThe graph shown represents a linear relationship between two variables, typically denoted as \( x \) (horizontal axis) and \( y \) (vertical axis).- **Axes and Grid:** - The horizontal axis (x-axis) is labeled from -6 to 6. - The vertical axis (y-axis) is labeled from -4 to 6. - Both axes are marked with evenly spaced grid lines for better visualization and accuracy of data points. - **Line Representation:** - The line on the graph starts at the point (-4, -2) and passes through to the point (4, 4). - This suggests a positive linear relationship, meaning as the value of \( x \) increases, the value of \( y \) also increases.#### Components of the Graph:1. **Origin:** The point where the x-axis and y-axis intersect is known as the origin, which is at the coordinate (0,0). 2. **Slope:** The slope of the line can be calculated by the formula: \[ \text{slope} = \frac{\Delta y}{\Delta x} \] , which is the change in \( y \) divided by the change in \( x \). Visually, it represents how steep the line is.3. **Intercepts:** - **Y-intercept:** The value where the line crosses the y-axis. For this graph, it appears this value might be around (-3,0), but we would need more data points. - **X-intercept:** The value where the line crosses the x-axis. For this graph, it seems to occur around (2.6,0).#### Conclusion:This linear graph is a simple yet powerful representation of how the y-variable changes as the x-variable changes. Understanding how to interpret and create such graphs is fundamental in many areas of mathematics, science, and engineering.

Answered: Image /qna-images/answer/52c1dc88-c7df-4067-a802-aa4005d13042.jpg

Answered: -2 -6- X G

-2 -6- X G

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...