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The function graphed is of the form y=a sin bx or y= a cos bx, where b>0. Determine the equation of the graph.

The function graphed is of the form y=a sin bx or y= a cos bx, where b>0. Determine the equation of the graph.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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The function graphed is of the form y=a sin bx or y= a cos bx, where b>0. Determine the equation of the graph.
Sure! Here is the transcribed content along with an explanation of the graph and its elements: --- **Understanding Linear Equations and Graphs** **Graph of a Linear Function** In this lesson, we will examine the graph of a specific linear function. The graph dated below visually represents the equation \( y = x^2 \), a fundamental nonlinear function where the output \( y \) is the square of the input \( x \). **Description of the Graph:** - **Coordinate System:** The graph is plotted on a standard Cartesian coordinate system with the \( x \)-axis (horizontal) and \( y \)-axis (vertical). Both axes are labeled appropriately with arrows indicating the positive direction. - **Scale:** The \( x \)-axis ranges from 0 to \( 2π \), while the \( y \)-axis ranges from -8 to 8. The graph includes grid lines to aid in locating points accurately. - **Function Plot:** The plotted curve intercepts the origin (0,0) and has key labeled points at \( π \) on the x-axis. At \( x = π \) and \( x = 2π \), the function provides corresponding \( y \)-values based on the square of the input \( x \). Each critical point such as \( π \) and \( 2π \) is marked on the graph for reference, indicating where the function hits these notable values. Understanding this graph helps in grasping the behavior of quadratic functions, their growth patterns, and their symmetric properties. **Key Points:** 1. **Intercept:** The graph passes through the origin (0,0). 2. **Shape:** The curve is a parabola opening upward since it plots a quadratic function. 3. **Critical Values:** Key points of \( π \) and \( 2π \) are marked on the \( x \)-axis, showing the function's values at these inputs. By analyzing and plotting these functions, you can better understand how changes in the input \( x \) affect the output \( y \) in quadratic equations. --- This explanation provides a detailed description and educational insight into the graph presented, suitable for an educational website.
Transcribed Image Text:Sure! Here is the transcribed content along with an explanation of the graph and its elements: --- **Understanding Linear Equations and Graphs** **Graph of a Linear Function** In this lesson, we will examine the graph of a specific linear function. The graph dated below visually represents the equation \( y = x^2 \), a fundamental nonlinear function where the output \( y \) is the square of the input \( x \). **Description of the Graph:** - **Coordinate System:** The graph is plotted on a standard Cartesian coordinate system with the \( x \)-axis (horizontal) and \( y \)-axis (vertical). Both axes are labeled appropriately with arrows indicating the positive direction. - **Scale:** The \( x \)-axis ranges from 0 to \( 2π \), while the \( y \)-axis ranges from -8 to 8. The graph includes grid lines to aid in locating points accurately. - **Function Plot:** The plotted curve intercepts the origin (0,0) and has key labeled points at \( π \) on the x-axis. At \( x = π \) and \( x = 2π \), the function provides corresponding \( y \)-values based on the square of the input \( x \). Each critical point such as \( π \) and \( 2π \) is marked on the graph for reference, indicating where the function hits these notable values. Understanding this graph helps in grasping the behavior of quadratic functions, their growth patterns, and their symmetric properties. **Key Points:** 1. **Intercept:** The graph passes through the origin (0,0). 2. **Shape:** The curve is a parabola opening upward since it plots a quadratic function. 3. **Critical Values:** Key points of \( π \) and \( 2π \) are marked on the \( x \)-axis, showing the function's values at these inputs. By analyzing and plotting these functions, you can better understand how changes in the input \( x \) affect the output \( y \) in quadratic equations. --- This explanation provides a detailed description and educational insight into the graph presented, suitable for an educational website.
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