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Does this graph represent a function? Explain how you know. 3 2 1 -1 -2 -3L 1 2 3 75 6 X MathBits.com

Does this graph represent a function? Explain how you know. 3 2 1 -1 -2 -3L 1 2 3 75 6 X MathBits.com

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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**Question 5** **2 pts** Does this graph represent a function? Explain how you know. **Graph Description:** The graph depicts a curve situated on a coordinate plane with axes labeled \(x\) and \(y\). The curve forms a sideways parabola opening to the right, spanning from approximately \(x = 0\) to \(x = 6\), and vertically from \(y = -3\) to \(y = 4\). The equation represented appears to be in the form of \(x = y^2\) or similar, indicating a relation where \(y\) values can correspond to more than one \(x\) value. **Analysis:** To determine if the graph represents a function, apply the vertical line test: If any vertical line drawn through the graph intersects the curve at more than one point, the graph does not represent a function. Given that this particular graph of a sideways parabola does intersect vertical lines at multiple points, it does not represent a function.
Transcribed Image Text:**Question 5** **2 pts** Does this graph represent a function? Explain how you know. **Graph Description:** The graph depicts a curve situated on a coordinate plane with axes labeled \(x\) and \(y\). The curve forms a sideways parabola opening to the right, spanning from approximately \(x = 0\) to \(x = 6\), and vertically from \(y = -3\) to \(y = 4\). The equation represented appears to be in the form of \(x = y^2\) or similar, indicating a relation where \(y\) values can correspond to more than one \(x\) value. **Analysis:** To determine if the graph represents a function, apply the vertical line test: If any vertical line drawn through the graph intersects the curve at more than one point, the graph does not represent a function. Given that this particular graph of a sideways parabola does intersect vertical lines at multiple points, it does not represent a function.
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