The graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct. Select all correct answers. Select all that apply: O As a → -2 , f(x) → -00 O As a → 1, f(x) → -∞ O As a → -0, f(x) → -2 O As a →1, f(x) → ∞ O As a → 00, f(x) → -2 O As a → 1', f(x) → -0∞
The graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct. Select all correct answers. Select all that apply: O As a → -2 , f(x) → -00 O As a → 1, f(x) → -∞ O As a → -0, f(x) → -2 O As a →1, f(x) → ∞ O As a → 00, f(x) → -2 O As a → 1', f(x) → -0∞
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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 and \( x = 1 \). As \( x \to -2^-\), the function approaches \(-\infty\), and as \( x \to -2^+\), the function approaches \(\infty\). As \( x \to 1^-\), the function approaches \(\infty\), and as \( x \to 1^+\), the function approaches \(-\infty\). The function has horizontal asymptotes at \( y = -2 \) as \( x \to \pm\infty \).)
Select all correct answers.
Select all that apply:
- [ ] As \( x \to -2^-, f(x) \to -\infty \)
- [ ] As \( x \to 1^-, f(x) \to -\infty \)
- [ ] As \( x \to -\infty, f(x) \to -2 \)
- [ ] As \( x \to 1^-, f(x) \to \infty \)
- [ ] As \( x \to \infty, f(x) \to -2 \)
- [ ] As \( x \to 1^+, f(x) \to -\infty \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe46867b-8e32-4051-86e0-c12e0211534e%2F9d67c757-2b76-4941-8c1b-cb642618b10e%2F87k1fqe_processed.png&w=3840&q=75)
Transcribed Image Text:The graph of the rational function \( f(x) \) is shown below. Using the graph, determine which of the following local and end behaviors are correct.
 and \( x = 1 \). As \( x \to -2^-\), the function approaches \(-\infty\), and as \( x \to -2^+\), the function approaches \(\infty\). As \( x \to 1^-\), the function approaches \(\infty\), and as \( x \to 1^+\), the function approaches \(-\infty\). The function has horizontal asymptotes at \( y = -2 \) as \( x \to \pm\infty \).)
Select all correct answers.
Select all that apply:
- [ ] As \( x \to -2^-, f(x) \to -\infty \)
- [ ] As \( x \to 1^-, f(x) \to -\infty \)
- [ ] As \( x \to -\infty, f(x) \to -2 \)
- [ ] As \( x \to 1^-, f(x) \to \infty \)
- [ ] As \( x \to \infty, f(x) \to -2 \)
- [ ] As \( x \to 1^+, f(x) \to -\infty \)
![**Identify the Rational Function**
The rational function's graph is given below. The x-intercept is \((1, 0)\) and the y-intercept is \((0, -1)\).
**Graph Explanation:**
- The purple curve is hyperbolic in nature, indicating a rational function with vertical and horizontal asymptotes.
- The curve approaches the vertical asymptote near \(x = -1\) from both sides.
- As \(x\) increases or decreases towards infinity, the curve gets closer to the horizontal axis (asymptotic behavior).
- This behavior suggests a hyperbola with transformed axes.
![Graph]()
**Select the correct answer below:**
- \( \circ \quad f(x) = \frac{x - 1}{x + 2} \)
- \( \circ \quad f(x) = \frac{x - 2}{x + 1} \)
- \( \circ \quad f(x) = \frac{x - 1}{x + 1} \)
- \( \circ \quad f(x) = \frac{x + 1}{-x + 1} \)
- \( \circ \quad f(x) = \frac{x + 1}{x - 1} \)
- \( \circ \quad f(x) = \frac{x - 1}{-x + 1} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe46867b-8e32-4051-86e0-c12e0211534e%2F9d67c757-2b76-4941-8c1b-cb642618b10e%2Fgn6zv3l_processed.png&w=3840&q=75)
Transcribed Image Text:**Identify the Rational Function**
The rational function's graph is given below. The x-intercept is \((1, 0)\) and the y-intercept is \((0, -1)\).
**Graph Explanation:**
- The purple curve is hyperbolic in nature, indicating a rational function with vertical and horizontal asymptotes.
- The curve approaches the vertical asymptote near \(x = -1\) from both sides.
- As \(x\) increases or decreases towards infinity, the curve gets closer to the horizontal axis (asymptotic behavior).
- This behavior suggests a hyperbola with transformed axes.
![Graph]()
**Select the correct answer below:**
- \( \circ \quad f(x) = \frac{x - 1}{x + 2} \)
- \( \circ \quad f(x) = \frac{x - 2}{x + 1} \)
- \( \circ \quad f(x) = \frac{x - 1}{x + 1} \)
- \( \circ \quad f(x) = \frac{x + 1}{-x + 1} \)
- \( \circ \quad f(x) = \frac{x + 1}{x - 1} \)
- \( \circ \quad f(x) = \frac{x - 1}{-x + 1} \)
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