Identify the rational function with smallest degree in the numerator and denominator whose graph matches the graph given below. The function has an x-intercept at x = -1 and a y-intercept at y = 2.
Identify the rational function with smallest degree in the numerator and denominator whose graph matches the graph given below. The function has an x-intercept at x = -1 and a y-intercept at y = 2.
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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![**Instructions:**
Identify the rational function with the smallest degree in the numerator and denominator whose graph matches the graph given below. The function has an \( x \)-intercept at \( x = -1 \) and a \( y \)-intercept at \( y = 2 \).
**Graph Description:**
The graph depicts a rational function with the following characteristics:
- The curve is defined from \( x = -7 \) to \( x = 7 \).
- The curve passes through the point \((-1, 0)\), indicating the \( x \)-intercept.
- The curve approaches a vertical asymptote near \( x = 0 \) and a horizontal asymptote near \( y = 2 \).
- The function appears to have a sharp increase near \( x = 0 \) and then decreases as \( x \) moves towards positive infinity.
**Provide your answer below:**
\[ f(x) = \text{(Your Answer Here)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532877df-e851-4773-88e1-aeed6288efee%2F9fda30b9-34d1-4e38-8f90-91f704785418%2F5528sgp_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Identify the rational function with the smallest degree in the numerator and denominator whose graph matches the graph given below. The function has an \( x \)-intercept at \( x = -1 \) and a \( y \)-intercept at \( y = 2 \).
**Graph Description:**
The graph depicts a rational function with the following characteristics:
- The curve is defined from \( x = -7 \) to \( x = 7 \).
- The curve passes through the point \((-1, 0)\), indicating the \( x \)-intercept.
- The curve approaches a vertical asymptote near \( x = 0 \) and a horizontal asymptote near \( y = 2 \).
- The function appears to have a sharp increase near \( x = 0 \) and then decreases as \( x \) moves towards positive infinity.
**Provide your answer below:**
\[ f(x) = \text{(Your Answer Here)} \]
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