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Does the graph represent a function that has an inverse function? A) No A) No B) Yes B) Yes

Does the graph represent a function that has an inverse function? A) No A) No B) Yes B) Yes

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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**Does the graph represent a function that has an inverse function?** *Graph Analysis:* 1. **First Graph:** - **Description:** The first graph shows a parabola that opens upwards. The curve is symmetric along the y-axis. - **Analysis:** This graph fails the horizontal line test, meaning any horizontal line drawn would intersect the graph at more than one point. Therefore, this function does not have an inverse function. - **Options:** - A) No - B) Yes - **Correct Answer:** A) No 2. **Second Graph:** - **Description:** The second graph depicts an S-shaped curve, resembling a cubic function, that continually increases across the graph. - **Analysis:** This graph passes the horizontal line test—any horizontal line would intersect the graph at most once. Therefore, this function does have an inverse function. - **Options:** - A) No - B) Yes - **Correct Answer:** B) Yes In summary, the first graph does not have an inverse function due to its failure to pass the horizontal line test, while the second graph does have an inverse function.
Transcribed Image Text:**Does the graph represent a function that has an inverse function?** *Graph Analysis:* 1. **First Graph:** - **Description:** The first graph shows a parabola that opens upwards. The curve is symmetric along the y-axis. - **Analysis:** This graph fails the horizontal line test, meaning any horizontal line drawn would intersect the graph at more than one point. Therefore, this function does not have an inverse function. - **Options:** - A) No - B) Yes - **Correct Answer:** A) No 2. **Second Graph:** - **Description:** The second graph depicts an S-shaped curve, resembling a cubic function, that continually increases across the graph. - **Analysis:** This graph passes the horizontal line test—any horizontal line would intersect the graph at most once. Therefore, this function does have an inverse function. - **Options:** - A) No - B) Yes - **Correct Answer:** B) Yes In summary, the first graph does not have an inverse function due to its failure to pass the horizontal line test, while the second graph does have an inverse function.
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