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

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Answer 1 · 2016-06-21T15:58:41

horizontal $y = -2/3$

vertical $x = -1/3$

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 $3x+1 = 0 \implies x = -1/3$

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