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Determine whether the following graph represents a function. -10 -8 -6 -4 -2 10 8 6 4 2 -4 -6 -8 y -10 6 8 10

Determine whether the following graph represents a function. -10 -8 -6 -4 -2 10 8 6 4 2 -4 -6 -8 y -10 6 8 10

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Determine whether the following graph represents a function.** **Graph Description:** The graph features a set of two smooth curves in the coordinate plane. These curves have a distinct hyperbolic shape and are positioned in four quadrants: 1. **Upper-left and Upper-right Quadrants:** - The curve rises steeply as it approaches \( y = 10 \), moving away horizontally from the y-axis. 2. **Lower-left and Lower-right Quadrants:** - The curve descends steeply as it approaches \( y = -10 \), moving horizontally towards the x-axis. **Axes and Grid:** - The graph is plotted on a coordinate grid with the x-axis ranging from \(-10\) to \(10\) and the y-axis ranging from \(-10\) to \(10\). - The x-axis and y-axis intersect at the origin \((0, 0)\). **Analysis:** - To determine if the graph represents a function, apply the vertical line test. - If any vertical line intersects the graph at more than one point, the graph does not represent a function. **Conclusion:** - The graph fails the vertical line test at \( x = 2 \) and \( x = -2 \), where a vertical line would intersect the graph at two points. - Therefore, the graph does not represent a function because one input (x-value) can correspond to multiple outputs (y-values).
Transcribed Image Text:**Determine whether the following graph represents a function.** **Graph Description:** The graph features a set of two smooth curves in the coordinate plane. These curves have a distinct hyperbolic shape and are positioned in four quadrants: 1. **Upper-left and Upper-right Quadrants:** - The curve rises steeply as it approaches \( y = 10 \), moving away horizontally from the y-axis. 2. **Lower-left and Lower-right Quadrants:** - The curve descends steeply as it approaches \( y = -10 \), moving horizontally towards the x-axis. **Axes and Grid:** - The graph is plotted on a coordinate grid with the x-axis ranging from \(-10\) to \(10\) and the y-axis ranging from \(-10\) to \(10\). - The x-axis and y-axis intersect at the origin \((0, 0)\). **Analysis:** - To determine if the graph represents a function, apply the vertical line test. - If any vertical line intersects the graph at more than one point, the graph does not represent a function. **Conclusion:** - The graph fails the vertical line test at \( x = 2 \) and \( x = -2 \), where a vertical line would intersect the graph at two points. - Therefore, the graph does not represent a function because one input (x-value) can correspond to multiple outputs (y-values).
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