A few days ago
Pre Calc Help?
f(x) = (4x-4) / (x^3 – 8)
What is the Horizontal Asymptote?
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A few days ago
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The horizontal asymptote is the horizontal line the graph approaches as x gets very large. Consider your numerator: as x gets enormous, the “-4” part really doesn’t matter. (If you had 400 billion dollars, would you be worried if you lost four of them?) So it approaches 4x. On the bottom, again as x gets large, the -8 doesn’t matter. So, as x gets large, the whole thing starts to look like 4x/(x^3), which reduces to 4/(x^2).
As x gets large, this fraction gets small. So the whole thing tends to 0, meaning that your horizontal asymptote is
y = 0
0
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