MHF-4U1-Problem-Solving-Assignment - MHF 4U1 Eric Zhang Problem Solving Assignment Rational Functions The function I have created is h x)= 45 x 4)2

# MHF-4U1-Problem-Solving-Assignment - MHF 4U1 Eric Zhang...

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MHF 4U1 Eric Zhang Problem Solving Assignment: Rational Functions The function I have created is: h ( x ) = 45 ( x + 4 ) 2 49 ( x + 6 ) ( where x ≠ 9 ) A graph is as follows: y = 45 49 ( x + 2 ) x =− 6 h ( x )
MHF 4U1 Eric Zhang Required Characteristics: a) has a linear oblique asymptote Linear oblique asymptotes exist when the order of x in the numerator is 1 greater than the order of x in the denominator. It is conclusive that h ( x ) has a linear oblique asymptote, as the order of x in the denominator is 1 while the numerator’s is 2. The asymptote can be determined through polynomial division: h ( x ) = 45 ( x + 4 ) 2 49 ( x + 6 ) = 180 49 ( x + 6 ) + 45 49 ( x + 2 ) , where the linear oblique asymptote is the quotient: y = 45 49 ( x + 2 ) . Thus, the function has a linear oblique asymptote. b) has a hole in quadrant III Since a condition for the function is x≠ 9 , there is a point of discontinuity (a ‘hole’) at x =− 9 . The limit as x→ 9 is lim x → 9 h ( x ) = 375 49 and so the hole is at (− 9, 375 49 ) .

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• Fall '15
• Rational function, linear oblique asymptote, Eric Zhang