Answer:
y = 3
Explanation:
You want the horizontal asymptote of the function y = (3x -6)/(x +2).
Horizontal asymptote
When the degrees of the numerator and denominator of a rational function are the same, the horizontal asymptote is the ratio of the highest-degree terms of numerator and denominator.
y = (3x)/(x) = 3
The horizontal asymptote is y = 3.
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Additional comment
This is the quotient of the indicated ratio:
y = (3x -6)/(x +2) = 3 -12/(x +2)
As x gets large, the fraction tends to zero, so the function tends to y = 3.
This same approach (finding the quotient) also works for slant asymptotes and asymptotes of other degrees.
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