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Use the Vertical Line Test to determine whether the curve is the graph of a function of x.

Use the Vertical Line Test to determine whether the curve is the graph of a function of x.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Vertical Line Test for Graphs of Functions In this exercise, you will use the Vertical Line Test to determine whether several curves are the graphs of functions of \( x \). The Vertical Line Test states that if any vertical line intersects a curve more than once, then the curve is not the graph of a function. #### (a) ![Rectangle](path/to/rectangle_image.png) - [ ] Is a function - [x] Is not a function **Explanation:** The rectangle's vertical sides intersect any vertical line at two points within the range of \( x \). Therefore, it fails the Vertical Line Test, meaning it is not a function. #### (b) ![Ellipse](path/to/ellipse_image.png) - [ ] Is a function - [x] Is not a function **Explanation:** The ellipse’s vertical arc intersects vertical lines at two places for most values of \( x \). This indicates it is not a function as it fails the Vertical Line Test. #### (c) ![Wavy \\shaped curve](path/to/curve_image.png) - [x] Is a function - [ ] Is not a function **Explanation:** The wavy-shaped curve passes the Vertical Line Test because every vertical line intersects the graph at most once, confirming it is a function. #### (d) ![Piecewise Function](path/to/piecewise_function_image.png) - [x] Is a function - [ ] Is not a function **Explanation:** The piecewise function, which looks like a combination of different curves or line segments, also passes the Vertical Line Test. Each vertical line intersects it just once, thus it is a function. ### Notes - **Function:** A relation where each value of \( x \) corresponds to exactly one value of \( y \). - **Vertical Line Test:** A visual way to determine if a curve is a graph of a function. If any vertical line intersects the curve at more than one point, the graph does not represent a function. Test your understanding by evaluating if the given curves would pass the Vertical Line Test and thus represent functions.
Transcribed Image Text:### Vertical Line Test for Graphs of Functions In this exercise, you will use the Vertical Line Test to determine whether several curves are the graphs of functions of \( x \). The Vertical Line Test states that if any vertical line intersects a curve more than once, then the curve is not the graph of a function. #### (a) ![Rectangle](path/to/rectangle_image.png) - [ ] Is a function - [x] Is not a function **Explanation:** The rectangle's vertical sides intersect any vertical line at two points within the range of \( x \). Therefore, it fails the Vertical Line Test, meaning it is not a function. #### (b) ![Ellipse](path/to/ellipse_image.png) - [ ] Is a function - [x] Is not a function **Explanation:** The ellipse’s vertical arc intersects vertical lines at two places for most values of \( x \). This indicates it is not a function as it fails the Vertical Line Test. #### (c) ![Wavy \\shaped curve](path/to/curve_image.png) - [x] Is a function - [ ] Is not a function **Explanation:** The wavy-shaped curve passes the Vertical Line Test because every vertical line intersects the graph at most once, confirming it is a function. #### (d) ![Piecewise Function](path/to/piecewise_function_image.png) - [x] Is a function - [ ] Is not a function **Explanation:** The piecewise function, which looks like a combination of different curves or line segments, also passes the Vertical Line Test. Each vertical line intersects it just once, thus it is a function. ### Notes - **Function:** A relation where each value of \( x \) corresponds to exactly one value of \( y \). - **Vertical Line Test:** A visual way to determine if a curve is a graph of a function. If any vertical line intersects the curve at more than one point, the graph does not represent a function. Test your understanding by evaluating if the given curves would pass the Vertical Line Test and thus represent functions.
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