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**Graph Analysis of a Rational Function** **Instruction:** Use the graph of the rational function to complete the following statement. **Statement:** As \( x \to -4^- \), \( f(x) \to \, \_\_\_\_ \) **Graph Description:** - The graph displays a rational function with a vertical asymptote at \( x = -4 \). - As \( x \) approaches \(-4\) from the left (\(x \to -4^-\)), the graph shows that \( f(x) \) tends towards negative infinity, i.e., \( f(x) \to -\infty \). - There is another vertical asymptote at \( x = 3 \). - The horizontal asymptote appears to be the x-axis (\(y = 0\)). **Answer Box:** As \( x \to -4^- \), \( f(x) \to -\infty \). **Instruction for Submission:** Enter your answer in the answer box and then click "Check Answer." **Note:** This exercise helps in understanding the behavior of rational functions near their asymptotes and the concept of limits.

**Graph Analysis of a Rational Function** **Instruction:** Use the graph of the rational function to complete the following statement. **Statement:** As \( x \to -4^- \), \( f(x) \to \, \_\_\_\_ \) **Graph Description:** - The graph displays a rational function with a vertical asymptote at \( x = -4 \). - As \( x \) approaches \(-4\) from the left (\(x \to -4^-\)), the graph shows that \( f(x) \) tends towards negative infinity, i.e., \( f(x) \to -\infty \). - There is another vertical asymptote at \( x = 3 \). - The horizontal asymptote appears to be the x-axis (\(y = 0\)). **Answer Box:** As \( x \to -4^- \), \( f(x) \to -\infty \). **Instruction for Submission:** Enter your answer in the answer box and then click "Check Answer." **Note:** This exercise helps in understanding the behavior of rational functions near their asymptotes and the concept of limits.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Graph Analysis of a Rational Function** **Instruction:** Use the graph of the rational function to complete the following statement. **Statement:** As \( x \to -4^- \), \( f(x) \to \, \_\_\_\_ \) **Graph Description:** - The graph displays a rational function with a vertical asymptote at \( x = -4 \). - As \( x \) approaches \(-4\) from the left (\(x \to -4^-\)), the graph shows that \( f(x) \) tends towards negative infinity, i.e., \( f(x) \to -\infty \). - There is another vertical asymptote at \( x = 3 \). - The horizontal asymptote appears to be the x-axis (\(y = 0\)). **Answer Box:** As \( x \to -4^- \), \( f(x) \to -\infty \). **Instruction for Submission:** Enter your answer in the answer box and then click "Check Answer." **Note:** This exercise helps in understanding the behavior of rational functions near their asymptotes and the concept of limits.
Transcribed Image Text:**Graph Analysis of a Rational Function** **Instruction:** Use the graph of the rational function to complete the following statement. **Statement:** As \( x \to -4^- \), \( f(x) \to \, \_\_\_\_ \) **Graph Description:** - The graph displays a rational function with a vertical asymptote at \( x = -4 \). - As \( x \) approaches \(-4\) from the left (\(x \to -4^-\)), the graph shows that \( f(x) \) tends towards negative infinity, i.e., \( f(x) \to -\infty \). - There is another vertical asymptote at \( x = 3 \). - The horizontal asymptote appears to be the x-axis (\(y = 0\)). **Answer Box:** As \( x \to -4^- \), \( f(x) \to -\infty \). **Instruction for Submission:** Enter your answer in the answer box and then click "Check Answer." **Note:** This exercise helps in understanding the behavior of rational functions near their asymptotes and the concept of limits.
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