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Create a rational function of the form: f(x) = · a(bx+j) (cx+k)(dx+m)² (ex+n) (gx-p)(hx+q) with the following conditions i) a,b,c,d,e,g h.,j,k,m,n,p.q are non-zero integers. ii) the three factors in the numerator must be different and the three factors in the denominator must be different, but some factors in the numerator can be the same as those in the denominator a,b,c,d,e,g,h can all be set to one if you like iv) f(x) has to have two different types of discontinuities and at least one crossover point Use your Curve Sketching Plan to fully characterize your function and draw an accurate sketch showing all significant features.

Create a rational function of the form: f(x) = · a(bx+j) (cx+k)(dx+m)² (ex+n) (gx-p)(hx+q) with the following conditions i) a,b,c,d,e,g h.,j,k,m,n,p.q are non-zero integers. ii) the three factors in the numerator must be different and the three factors in the denominator must be different, but some factors in the numerator can be the same as those in the denominator a,b,c,d,e,g,h can all be set to one if you like iv) f(x) has to have two different types of discontinuities and at least one crossover point Use your Curve Sketching Plan to fully characterize your function and draw an accurate sketch showing all significant features.

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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Create a rational function of the form: f(x) = · a(bx+j) (cx+k)(dx+m)² (ex+n) (gx-p)(hx+q) with the following conditions i) a,b,c,d,e,g h.,j,k,m,n,p.q are non-zero integers. ii) the three factors in the numerator must be different and the three factors in the denominator must be different, but some factors in the numerator can be the same as those in the denominator a,b,c,d,e,g,h can all be set to one if you like iv) f(x) has to have two different types of discontinuities and at least one crossover point Use your Curve Sketching Plan to fully characterize your function and draw an accurate sketch showing all significant features.
Transcribed Image Text:Create a rational function of the form: f(x) = · a(bx+j) (cx+k)(dx+m)² (ex+n) (gx-p)(hx+q) with the following conditions i) a,b,c,d,e,g h.,j,k,m,n,p.q are non-zero integers. ii) the three factors in the numerator must be different and the three factors in the denominator must be different, but some factors in the numerator can be the same as those in the denominator a,b,c,d,e,g,h can all be set to one if you like iv) f(x) has to have two different types of discontinuities and at least one crossover point Use your Curve Sketching Plan to fully characterize your function and draw an accurate sketch showing all significant features.
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