3. `y=(x+2)/(x^2+2x-8)`, find Asymptotes of a function
Solution:
Asymptotes :
Now, find domain of `y=(x+2)/(x^2+2x-8)`
`y=(x+2)/(x^2+2x-8)`
`x^2+2x-8=0`
`=>x^2+2x-8=0`
`=>x^2-2x+4x-8 = 0`
`=>x(x-2)+4(x-2) = 0`
`=>(x-2)(x+4) = 0`
`=>(x-2) = 0" or "(x+4) = 0`
`=>x = 2" or "x = -4`
Domain : `x!=2,x!=-4`
Vertical asymptote : `x=2,x=-4`
The highest power in the numerator is 1
The highest power in the denominator is 2
Since highest power denominator is greater than highest power on numerator, then the horizontal asymptote will be x-axis.
Horizontal asymptote : y = 0 (x-axis)
Slant(Oblique) asymptote : none
This material is intended as a summary. Use your textbook for detail explanation.
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