CBSE Class 11-science Answered

Can the graph of a rational function coincide with its slant asymptote?

Asked by Varunasav | 28 Sep, 2014, 11:25: AM

Expert Answer

C o n s i d e r space t h e space r a t i o n a l space f u n c t i o n comma y equals fraction numerator x squared minus 2 x plus 1 over denominator x plus 2 end fraction T h e space g r a p h space o f space t h e space a b o v e space f u n c t i o n space i s space a s space f o l l o w s :

A t space x equals minus 2 comma space t h e r e space i s space a space v e r t i c a l space a s y m p t o t e.

A s space x space i n c r e a s e s comma space t h e space s a m e space g r a p h space a p p e a r s space a s space f o l l o w s :

F r o m space t h e space g r a p h space w e space c a n space s e e space t h a t space t h e r e space i s space a space s h a r p space b e n d space i n space t h e space c u r v e space n e a r space y minus a x i s. B y space d i v s i o n space a l g o r i t h m comma space w e space h a v e comma fraction numerator x squared minus 2 x plus 1 over denominator x plus 2 end fraction equals x minus 4 plus fraction numerator 9 over denominator x plus 2 end fraction N o w comma space f o r space l a r g e r space v a l u e s space o f space x comma space w e space h a v e comma limit as x rightwards arrow infinity of fraction numerator x squared minus 2 x plus 1 over denominator x plus 2 end fraction equals limit as x rightwards arrow infinity of x minus 4 plus limit as x rightwards arrow infinity of fraction numerator 9 over denominator x plus 2 end fraction A s comma space limit as x rightwards arrow infinity of fraction numerator 9 over denominator x plus 2 end fraction equals 0 comma space w e space h a v e comma fraction numerator x squared minus 2 x plus 1 over denominator x plus 2 end fraction equals x minus 4 T h u s comma space t h e space l i n e a r space e q u a t i o n space y equals x minus 4 space i s space a n space o b l i q u e space a s y m p t o t e. T h u s comma space a t space t h e space v e r t i c a l space a s y m p t o t e comma space x equals minus 2 comma space t h e space g r a p h space o f space t h e space o r i g i n a l space f u n c t i o n fraction numerator x squared minus 2 x plus 1 over denominator x plus 2 end fraction space l o o k s space l i k e space t h e space p r o p e r space f u n c t i o n space fraction numerator 9 over denominator x plus 2 end fraction O b s e r v e space t h e space f o l l o w i n g space g r a p h :

Answered by Vimala Ramamurthy | 29 Sep, 2014, 11:33: AM

CBSE Class 11-science Answered

Concept Videos

Ordered pairs, cartesian products of sets

Relation between two sets

Functions and various forms of representation

Graphs of special types of functions

Ordered pair and cartesian product of sets

CALL US / WHATSAPP

Please Login or Sign up to continue!

CBSE Class 11-science Answered

Concept Videos

Ordered pairs, cartesian products of sets

Relation between two sets

Functions and various forms of representation

Graphs of special types of functions

Ordered pair and cartesian product of sets

Choose Filters

Open In Ask A Doubt App ?

Get in Touch

Call / Whats App