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2. Suppose f(x) is a rational function with leading term -1, has three roots: a root at z = -2 of degree 1, a root at z = 0 of degree 1, and a root at z - 1 of degree 1, f(a) also has a vertical asymptote at z=-1 of degree 3. (a) Determine the sign decomposition of f(x): (b) Graph f(a): (e) (extra credit) Find a rational function with the same properties as f(x).

2. Suppose f(x) is a rational function with leading term -1, has three roots: a root at z = -2 of degree 1, a root at z = 0 of degree 1, and a root at z - 1 of degree 1, f(a) also has a vertical asymptote at z=-1 of degree 3. (a) Determine the sign decomposition of f(x): (b) Graph f(a): (e) (extra credit) Find a rational function with the same properties as f(x).

Advanced Engineering Mathematics
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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2. Suppose f(x) is a rational function with leading term -1, has three roots: a root at z=-2 of degree 1, a root at z = 0 of degree 1, and a root at z 1 of degree 1, f(z) also has a vertical asymptote at z=-1 of degree 3. (a) Determine the sign decomposition of f(x): (b) Graph f(z): (e) (extra credit) Find a rational function with the same properties as f(x).
Transcribed Image Text:2. Suppose f(x) is a rational function with leading term -1, has three roots: a root at z=-2 of degree 1, a root at z = 0 of degree 1, and a root at z 1 of degree 1, f(z) also has a vertical asymptote at z=-1 of degree 3. (a) Determine the sign decomposition of f(x): (b) Graph f(z): (e) (extra credit) Find a rational function with the same properties as f(x).
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