Asked by htht
The graph of f(x)= (6-4x)^2 / 2x^2 -5x +12 has a horizontal asymptote at y =
8
.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret f(x) as f(x) = (6 − 4x)^2 / (2x^2 − 5x + 12). For large |x| the highest-degree terms dominate, so compute the limit:
f(x) = ((6 − 4x)^2)/(2x^2 − 5x + 12)
= ((-4 + 6/x)^2)/(2 − 5/x + 12/x^2).
As x → ±∞ the terms with 1/x go to 0, so
lim_{x→±∞} f(x) = (-4)^2 / 2 = 16/2 = 8.
Thus the horizontal asymptote is y = 8.
f(x) = ((6 − 4x)^2)/(2x^2 − 5x + 12)
= ((-4 + 6/x)^2)/(2 − 5/x + 12/x^2).
As x → ±∞ the terms with 1/x go to 0, so
lim_{x→±∞} f(x) = (-4)^2 / 2 = 16/2 = 8.
Thus the horizontal asymptote is y = 8.
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