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АУ 10 F(X) X 10

АУ 10 F(X) X 10

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section: Chapter Questions
Problem 74SGR
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### Horizontal Shifting of Graphs The graph to the right was created by horizontally shifting the graph of the basic function \( y = \frac{1}{x} \). Write a function that describes the graph shown to the right. #### Explanation of the Graph The provided graph is plotted on a standard coordinate plane. Here are the detailed observations: - **Axes:** The \( x \)-axis and \( y \)-axis intersect at the origin. - **Grid:** The background is a grid, providing a clearer view of the increments. - **Curve:** The blue curve labeled \( f(x) \) demonstrates a hyperbolic shape typical of inverse functions. The key characteristic of this graph is that it represents a horizontal shift of the basic hyperbolic function \( y = \frac{1}{x} \). - The original curve of \( y = \frac{1}{x} \) has asymptotes at \( x=0 \). - The shifted curve \( f(x) \) appears to have its vertical asymptote now at \( x = 3 \), indicating the entire curve has been moved 3 units to the right. #### Question The function that describes the graph is \( f(x) = \boxed{\frac{1}{x-3}} \). (Simplify your answer.)
Transcribed Image Text:### Horizontal Shifting of Graphs The graph to the right was created by horizontally shifting the graph of the basic function \( y = \frac{1}{x} \). Write a function that describes the graph shown to the right. #### Explanation of the Graph The provided graph is plotted on a standard coordinate plane. Here are the detailed observations: - **Axes:** The \( x \)-axis and \( y \)-axis intersect at the origin. - **Grid:** The background is a grid, providing a clearer view of the increments. - **Curve:** The blue curve labeled \( f(x) \) demonstrates a hyperbolic shape typical of inverse functions. The key characteristic of this graph is that it represents a horizontal shift of the basic hyperbolic function \( y = \frac{1}{x} \). - The original curve of \( y = \frac{1}{x} \) has asymptotes at \( x=0 \). - The shifted curve \( f(x) \) appears to have its vertical asymptote now at \( x = 3 \), indicating the entire curve has been moved 3 units to the right. #### Question The function that describes the graph is \( f(x) = \boxed{\frac{1}{x-3}} \). (Simplify your answer.)
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