2. `y=(x^2+2x-3)/(x^2-5x-6)`, find Asymptotes of a function
Solution:
Asymptotes :
Now, find domain of `y=(x^2+2x-3)/(x^2-5x-6)`
`y=(x^2+2x-3)/(x^2-5x-6)`
`x^2-5x-6=0`
`=>x^2-5x-6=0`
`=>x^2+x-6x-6 = 0`
`=>x(x+1)-6(x+1) = 0`
`=>(x+1)(x-6) = 0`
`=>(x+1) = 0" or "(x-6) = 0`
`=>x = -1" or "x = 6`
Domain : `x!=-1,x!=6`
Vertical asymptote : `x=-1,x=6`
The highest power in the numerator is 2
The highest power in the denominator is 2
Horizontal asymptote : `y=1`
Slant(Oblique) asymptote : none
This material is intended as a summary. Use your textbook for detail explanation.
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