Answer:
Explanation:
Start with the vertical asymptote
It occurs at the value where the denominator = 0
The denominator factors
3x^2 - 5x - 12 = 0 in two place
(3x + 4)(x - 3)
x - 3 = 0
x = 3
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3x + 4 = 0
3x = - 4
x = - 4/3
Either one of these values will give a vertical asymptote.
Horizontal Asymptote
The horizontal asymptotes are just the coefficients in front of the equal powers at the front of both the top and bottom polynomials.
In this case, the answer is y = 2/3 (you will get a horizontal asymptote approaching y = 2/3
The complete graph is shown below.
The vertical asymptote at 3 is absent because there is a horizontal one at y = 2/3