Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `g(x)= (-2x+3) /( 3x+1)`?

Answer 1

horizontal `y = -2/3`

vertical `x = -1/3`

Explanation:

testing for horizontal or oblique

`(-2x+3)/(3x+1) ]_{x \to pm \infty}`

`= (-2+3/x)/(3+1/x) ]_{x \to pm \infty} = -2/3`

for vertical , we look at denominator = 0

so `3x+1 = 0 \implies x = -1/3`