2 and 3 x'- 3x+1Consider the function f defined on R - {2} as: f x1and let (C) be its-= x -1-x- 2x- 2representative curve in an orthonormal system of axes x' 0 x;y' 0y.1) a - Prove that the straight line (d 1) of equation x= 2 is an asymptote to (C).b- Prove that the straight line (d 2) of equation y = x- 1 is an asymptote to (C).a- Prove that the point of intersection of (d 1) and (d 2) is the center of symmetry of (C).x'- 4x+52) a- Prove that : f' x =.x-2b- Set up the table of variations of f.3) Draw (C).

Name: 2 and 3 x'- 3x+1Consider the function f defined on R - {2} as: f x1and
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Description: 2 and 3 x'- 3x+1Consider the function f defined on R - {2} as: f x1and let (C) be its-= x -1-x- 2x- 2representative curve in an orthonormal system of axes x' 0 x;y' 0y.1) a - Prove that the straight line (d 1) of equation x= 2 is an asymptote to (C).

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Answered: x -4x +5 - Prove that: f' x x-2

Math

Advanced Math

x -4x +5 - Prove that: f' x x-2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 51E

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Question

2 and 3

x'- 3x+1
Consider the function f defined on R - {2} as: f x
1
and let (C) be its
-= x -1-
x- 2
x- 2
representative curve in an orthonormal system of axes x' 0 x;y' 0y.
1) a - Prove that the straight line (d 1) of equation x= 2 is an asymptote to (C).
b- Prove that the straight line (d 2) of equation y = x- 1 is an asymptote to (C).
a- Prove that the point of intersection of (d 1) and (d 2) is the center of symmetry of (C).
x'- 4x+5
2) a- Prove that : f' x =.
x-2
b- Set up the table of variations of f.
3) Draw (C).

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