The figure below shows the graph of a rational function f. It has vertical asymptotes x=-2 and x = 4, and horizontal asymptote y = -2. The graph has x-intercepts -4 and.1, and it passes through the point (0, -1). 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. I Of(x) = Of(x) = Of(x) = Of(x): Of(x) = = a x - b 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) 10 1 00 10 00 100 - 00 =
The figure below shows the graph of a rational function f. It has vertical asymptotes x=-2 and x = 4, and horizontal asymptote y = -2. The graph has x-intercepts -4 and.1, and it passes through the point (0, -1). 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. I Of(x) = Of(x) = Of(x) = Of(x): Of(x) = = a x - b 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) 10 1 00 10 00 100 - 00 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The figure below shows the graph of a rational function \( f \).
It has vertical asymptotes \( x = -2 \) and \( x = 4 \), and horizontal asymptote \( y = -2 \).
The graph has \( x \)-intercepts \(-4\) and \(1\), and it passes through the point \((0, -1)\).
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.
The graph is depicted below. It consists of two distinct branches: the first exhibiting a hyperbolic shape passing through \((-4,0)\) and \((1,0)\) with vertical asymptotes as dashed lines at \( x = -2 \) and \( x = 4 \), and horizontal asymptote as a dashed line at \( y = -2 \). The graph also passes through the point \((0, -1)\).
\[
\begin{array}{rl}
\circ & f(x) = \frac{a}{x - b} = \\
\circ & f(x) = \frac{a(x - b)}{x - c} = \\
\circ & f(x) = \frac{a}{(x - b)(x - c)} = \bigcirc \bigcirc \\
\circ & f(x) = \frac{a(x - b)}{(x - c)(x - d)} = \bigcirc \bigcirc \circ\\
\circ & f(x) = \frac{a(x - b)(x - c)}{(x - d)(x - e)} = \bigcirc \bigcirc \circ \bigcirc \bigcirc \\
\end{array}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae73a37-719e-4892-8745-1f816a181ea7%2F81a814df-797e-480b-86b8-4c6852a566dc%2F2zugf1f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The figure below shows the graph of a rational function \( f \).
It has vertical asymptotes \( x = -2 \) and \( x = 4 \), and horizontal asymptote \( y = -2 \).
The graph has \( x \)-intercepts \(-4\) and \(1\), and it passes through the point \((0, -1)\).
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.
The graph is depicted below. It consists of two distinct branches: the first exhibiting a hyperbolic shape passing through \((-4,0)\) and \((1,0)\) with vertical asymptotes as dashed lines at \( x = -2 \) and \( x = 4 \), and horizontal asymptote as a dashed line at \( y = -2 \). The graph also passes through the point \((0, -1)\).
\[
\begin{array}{rl}
\circ & f(x) = \frac{a}{x - b} = \\
\circ & f(x) = \frac{a(x - b)}{x - c} = \\
\circ & f(x) = \frac{a}{(x - b)(x - c)} = \bigcirc \bigcirc \\
\circ & f(x) = \frac{a(x - b)}{(x - c)(x - d)} = \bigcirc \bigcirc \circ\\
\circ & f(x) = \frac{a(x - b)(x - c)}{(x - d)(x - e)} = \bigcirc \bigcirc \circ \bigcirc \bigcirc \\
\end{array}
\]
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