8/15/2014 For very large values of x, the graph of f(x) = x² / (x + 1) behaves as that of a line y = mx + b. Find m and b.

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8/15/2014 Solution. Since the degree of the numerator in f(x) = x² / (x + 1) is 1 more than that of the denominator, f(x) has no horizontal asymptotes. However, it has a slant / oblique asymptote. To find this, simply divide x² by (x + 1) to get:

f(x) = (x – 1) + 1/x².

Now, as x → ∞, f(x) → x – 1.

Therefore, the line is y = 1x – 1 with m = 1, b = -1.