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The figure below shows the graph of a rational function f. It has vertical asymptotes x=5 and x=-6, and horizontal asymptote y=0. The graph has x-intercept -3, and it passes through the point (-7, 2). The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f(x), and then write the equation. You can assume that f(x) is in simplest form. -(-7,2) Of(x) Of(x) = Of(x) = Of(x) = Of(x) = = X a - a (x - b) X - C a (x - b) (x - c) a (x - b) (x - c)(x - d) a(x −b)(x - c) (x - d) (x - e) II DIO OI II = _ = 00 0 00 D(0) 00 100 00

The figure below shows the graph of a rational function f. It has vertical asymptotes x=5 and x=-6, and horizontal asymptote y=0. The graph has x-intercept -3, and it passes through the point (-7, 2). The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f(x), and then write the equation. You can assume that f(x) is in simplest form. -(-7,2) Of(x) Of(x) = Of(x) = Of(x) = Of(x) = = X a - a (x - b) X - C a (x - b) (x - c) a (x - b) (x - c)(x - d) a(x −b)(x - c) (x - d) (x - e) II DIO OI II = _ = 00 0 00 D(0) 00 100 00

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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**Description:** The image presents a graph of a rational function \( f \). The key features described are: - **Vertical asymptotes** at \( x = 5 \) and \( x = -6 \). - **Horizontal asymptote** at \( y = 0 \). - **x-intercept** at \( x = -3 \). - The graph passes through the point \((-7, 2)\). The task is to identify the form of \( f(x) \) from a list of rational functions and then determine the equation. It's given that \( f(x) \) is in its simplest form. **Graph Analysis:** The graph is divided into several parts: - Curves approaching the vertical lines \( x = 5 \) and \( x = -6 \) from above or below, indicating vertical asymptotes. - A branch passing through the x-axis at \( x = -3 \), representing an x-intercept. - The horizontal behavior near the x-axis suggests a horizontal asymptote at \( y = 0 \). **Function Forms:** The image provides different forms of rational functions: 1. \( f(x) = \frac{a}{x-b} \) 2. \( f(x) = \frac{a(x-b)}{x-c} \) 3. \( f(x) = \frac{a}{(x-b)(x-c)} \) 4. \( f(x) = \frac{a(x-b)}{(x-c)(x-d)} \) 5. \( f(x) = \frac{a(x-b)(x-c)}{(x-d)(x-e)} \) These forms have empty boxes for parameters \( a, b, c, d, \) and \( e \) to be filled based on the graph features. **Instructions:** Choose the appropriate rational function form and fill in the parameters to match the asymptotes, x-intercept, and point \((-7, 2)\) based on the graph.
Transcribed Image Text:**Description:** The image presents a graph of a rational function \( f \). The key features described are: - **Vertical asymptotes** at \( x = 5 \) and \( x = -6 \). - **Horizontal asymptote** at \( y = 0 \). - **x-intercept** at \( x = -3 \). - The graph passes through the point \((-7, 2)\). The task is to identify the form of \( f(x) \) from a list of rational functions and then determine the equation. It's given that \( f(x) \) is in its simplest form. **Graph Analysis:** The graph is divided into several parts: - Curves approaching the vertical lines \( x = 5 \) and \( x = -6 \) from above or below, indicating vertical asymptotes. - A branch passing through the x-axis at \( x = -3 \), representing an x-intercept. - The horizontal behavior near the x-axis suggests a horizontal asymptote at \( y = 0 \). **Function Forms:** The image provides different forms of rational functions: 1. \( f(x) = \frac{a}{x-b} \) 2. \( f(x) = \frac{a(x-b)}{x-c} \) 3. \( f(x) = \frac{a}{(x-b)(x-c)} \) 4. \( f(x) = \frac{a(x-b)}{(x-c)(x-d)} \) 5. \( f(x) = \frac{a(x-b)(x-c)}{(x-d)(x-e)} \) These forms have empty boxes for parameters \( a, b, c, d, \) and \( e \) to be filled based on the graph features. **Instructions:** Choose the appropriate rational function form and fill in the parameters to match the asymptotes, x-intercept, and point \((-7, 2)\) based on the graph.
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