The figure displays the graph of a rational function \( f(x) \). The graph has vertical asymptotes at \( x = -2 \) and \( x = 3 \), with a horizontal asymptote at \( y = 0 \). The x-intercept is at \( (1,0) \), and the graph passes through the point \( (-1,2) \).**Remark**: The problem is in ALEKS, "The x-intercept has odd multiplicity. Use the value of 1, because ALEKS does not recognize odd multiplicities larger than 1."### Graph Explanation:- **Vertical Asymptotes**: Indicated by dashed lines at \( x = -2 \) and \( x = 3 \). The graph approaches but never touches these lines.- **Horizontal Asymptote**: Indicated by a dashed line along \( y = 0 \). As \( x \) approaches positive or negative infinity, the graph approaches the x-axis.- **Point on the Graph**: A marked point at \( (-1,2) \), which is crucial for determining the equation.- **X-Intercept**: Occurs at \( (1,0) \), where the graph crosses the x-axis.**Question**: Determine an equation of the function, \( f(x) \), using the point \( (-1,2) \).

Answered: Image /qna-images/answer/efcc8a46-31f3-4c06-ba56-be242d94475a.jpg

Figure below shows the graph of a rational function f(x). It has vertical asymptotes at x = -2 and x = 3, and a horizontal asymptote y = 0. The coordinates of the x-intercept is (1,0), and it passes through the point (-1,2). (Remark: The problem is in ALEKS, "The x-intercept has odd multiplicity. Use the value of 1, because ALEKS does not recognize odd multiplicities larger than 1".) 10 5 (-1,2) + -10 -5 0 5 -5 10 Determine an equation of the function, f(x), using the point (-1,2).

Figure below shows the graph of a rational function f(x). It has vertical asymptotes at x = -2 and x = 3, and a horizontal asymptote y = 0. The coordinates of the x-intercept is (1,0), and it passes through the point (-1,2). (Remark: The problem is in ALEKS, "The x-intercept has odd multiplicity. Use the value of 1, because ALEKS does not recognize odd multiplicities larger than 1".) 10 5 (-1,2) + -10 -5 0 5 -5 10 Determine an equation of the function, f(x), using the point (-1,2).

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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Question

The figure displays the graph of a rational function \( f(x) \). The graph has vertical asymptotes at \( x = -2 \) and \( x = 3 \), with a horizontal asymptote at \( y = 0 \). The x-intercept is at \( (1,0) \), and the graph passes through the point \( (-1,2) \).

**Remark**: The problem is in ALEKS, "The x-intercept has odd multiplicity. Use the value of 1, because ALEKS does not recognize odd multiplicities larger than 1."

### Graph Explanation:
- **Vertical Asymptotes**: Indicated by dashed lines at \( x = -2 \) and \( x = 3 \). The graph approaches but never touches these lines.
- **Horizontal Asymptote**: Indicated by a dashed line along \( y = 0 \). As \( x \) approaches positive or negative infinity, the graph approaches the x-axis.
- **Point on the Graph**: A marked point at \( (-1,2) \), which is crucial for determining the equation.
- **X-Intercept**: Occurs at \( (1,0) \), where the graph crosses the x-axis.

**Question**: Determine an equation of the function, \( f(x) \), using the point \( (-1,2) \).

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