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The function f(x) is shown in the graph. Which type of function describes f(x)?

The function f(x) is shown in the graph. Which type of function describes f(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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Question

The function f(x) is shown in the graph.

Which type of function describes f(x)?

The image displays the graph of a function \( f(x) \), which appears to be a rational function due to its asymptotic behavior. Here's a detailed explanation: ### Graph Overview - **Axes**: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - **Function Behavior**: - The function consists of two distinct branches. - There is a vertical asymptote at \( x = 0 \), where the function is undefined. - The left branch is in the second and third quadrants, indicating that as \( x \) approaches 0 from the negative side, \( f(x) \) goes towards negative infinity. As \( x \) decreases further (more negative), \( f(x) \) approaches 0. - The right branch is in the first and fourth quadrants, indicating that as \( x \) approaches 0 from the positive side, \( f(x) \) goes towards positive infinity. As \( x \) increases, \( f(x) \) also increases. - **Axes Scales**: - The graph grid lines are marked with intervals of 1 on both axes. - The \( x \)-axis ranges from \(-8\) to \(8\). - The \( y \)-axis ranges from \(-8\) to \(8\). This graph visually represents the behavior typical of a rational function with a vertical asymptote at \( x = 0 \).
Transcribed Image Text:The image displays the graph of a function \( f(x) \), which appears to be a rational function due to its asymptotic behavior. Here's a detailed explanation: ### Graph Overview - **Axes**: - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - **Function Behavior**: - The function consists of two distinct branches. - There is a vertical asymptote at \( x = 0 \), where the function is undefined. - The left branch is in the second and third quadrants, indicating that as \( x \) approaches 0 from the negative side, \( f(x) \) goes towards negative infinity. As \( x \) decreases further (more negative), \( f(x) \) approaches 0. - The right branch is in the first and fourth quadrants, indicating that as \( x \) approaches 0 from the positive side, \( f(x) \) goes towards positive infinity. As \( x \) increases, \( f(x) \) also increases. - **Axes Scales**: - The graph grid lines are marked with intervals of 1 on both axes. - The \( x \)-axis ranges from \(-8\) to \(8\). - The \( y \)-axis ranges from \(-8\) to \(8\). This graph visually represents the behavior typical of a rational function with a vertical asymptote at \( x = 0 \).
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