Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Transformation of Graphs
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Question
What is the equation for​ g?
 
g(x)=
The image above displays a Cartesian coordinate system with two functions plotted: \(f(x)\) and \(g(x)\). 1. **Axes:** - The horizontal axis is labeled \(x\), and the vertical axis is labeled \(y\). - Both axes range from -10 to 10. 2. **Function \(f(x)\):** - The function \(f(x)\) is represented by the equation \(f(x) = \sqrt{x}\). - This function is shown using a black curve. The curve starts from the origin (0,0) and progresses to the right, rising gradually as \(x\) increases. 3. **Function \(g(x)\):** - The function \(g(x)\) is labeled as \(g(x)\) in blue. - The blue curve representing \(g(x)\) starts from a point below the origin and generally decreases as \(x\) increases. Details about the specific equation representing \(g(x)\) are not provided in the image. 4. **Grid:** - The background consists of a grid that allows for an accurate depiction of how the values of \(x\) and \(y\) change. Each grid line marks a unit which helps in identifying the coordinates of points on the curves for \(f(x)\) and \(g(x)\). The OK button below the graph suggests that this image might be interactive, providing users the option to confirm their understanding or proceed with the information provided. Understanding how different functions behave graphically is crucial in mathematics, as it provides insights into their properties and how they change in response to different inputs.
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Transcribed Image Text:The image above displays a Cartesian coordinate system with two functions plotted: \(f(x)\) and \(g(x)\). 1. **Axes:** - The horizontal axis is labeled \(x\), and the vertical axis is labeled \(y\). - Both axes range from -10 to 10. 2. **Function \(f(x)\):** - The function \(f(x)\) is represented by the equation \(f(x) = \sqrt{x}\). - This function is shown using a black curve. The curve starts from the origin (0,0) and progresses to the right, rising gradually as \(x\) increases. 3. **Function \(g(x)\):** - The function \(g(x)\) is labeled as \(g(x)\) in blue. - The blue curve representing \(g(x)\) starts from a point below the origin and generally decreases as \(x\) increases. Details about the specific equation representing \(g(x)\) are not provided in the image. 4. **Grid:** - The background consists of a grid that allows for an accurate depiction of how the values of \(x\) and \(y\) change. Each grid line marks a unit which helps in identifying the coordinates of points on the curves for \(f(x)\) and \(g(x)\). The OK button below the graph suggests that this image might be interactive, providing users the option to confirm their understanding or proceed with the information provided. Understanding how different functions behave graphically is crucial in mathematics, as it provides insights into their properties and how they change in response to different inputs.
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