Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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What is the graph? Domain & Range? please help??

**Graph the Function Using Transformations** Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function. \[ h(x) = \sqrt{x} + 2 \]
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Transcribed Image Text:**Graph the Function Using Transformations** Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function. \[ h(x) = \sqrt{x} + 2 \]
The image displays a graph of the function \( y = \sqrt{x} \). Below is a detailed explanation: ### Description of the Graph: - **Axes**: The graph is plotted on a Cartesian plane with the horizontal axis labeled as \( x \) and the vertical axis labeled as \( y \). Both axes range from \(-12\) to \(12\). - **Curve**: The function \( y = \sqrt{x} \) is depicted as a curve starting at the origin (0,0) and extending towards the right. The curve is only defined for non-negative values of \( x \) (i.e., \( x \geq 0 \)) since the square root of a negative number is not a real number. - **Direction**: The curve rises slowly as it moves to the right, indicating that as \( x \) increases, \( y \) (i.e., \( \sqrt{x} \)) also increases, but at a decreasing rate. - **Key Points**: No specific key points are marked on the graph, but it is clear that the curve passes through the origin. ### Characteristics of the Function: - **Domain**: \( x \geq 0 \) - **Range**: \( y \geq 0 \) - **Intercept**: The graph intersects the origin (0,0). This graphical representation is useful for visualizing how the square root function behaves, illustrating its increasing nature and showing its restriction to non-negative values of \( x \).
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Transcribed Image Text:The image displays a graph of the function \( y = \sqrt{x} \). Below is a detailed explanation: ### Description of the Graph: - **Axes**: The graph is plotted on a Cartesian plane with the horizontal axis labeled as \( x \) and the vertical axis labeled as \( y \). Both axes range from \(-12\) to \(12\). - **Curve**: The function \( y = \sqrt{x} \) is depicted as a curve starting at the origin (0,0) and extending towards the right. The curve is only defined for non-negative values of \( x \) (i.e., \( x \geq 0 \)) since the square root of a negative number is not a real number. - **Direction**: The curve rises slowly as it moves to the right, indicating that as \( x \) increases, \( y \) (i.e., \( \sqrt{x} \)) also increases, but at a decreasing rate. - **Key Points**: No specific key points are marked on the graph, but it is clear that the curve passes through the origin. ### Characteristics of the Function: - **Domain**: \( x \geq 0 \) - **Range**: \( y \geq 0 \) - **Intercept**: The graph intersects the origin (0,0). This graphical representation is useful for visualizing how the square root function behaves, illustrating its increasing nature and showing its restriction to non-negative values of \( x \).
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