Question 1059024
3x^3-17x^2+5x/x^5-2x
The first term in the numerator divided by the first term in the denominator is 3/x^2.  As x increases without bound, the value is 0. The horizontal asymptote is 0. While it appears that it approaches only from the negative side when x is positive, it does cross the x-axis on the right before gradually approaching 0.
{{{graph(300,300,-10,10,-10,10,(3x^3-17x^2+5x)/(x^5-2x))}}}
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5x^2-2x-5/8x^2+x+4
The ratio of the first term in both the numerator and the denominator is 5/8. When x gets large, only the term with the highest power matters.
{{{graph(300,300,-10,10,-10,10,(5x^2-2x-5)/(8x^2+x+4))}}}