**8/15/2014
**For
very large values of x, the graph of f(x) = x^{2}
/ (x + 1) behaves as that of a line y = *m*x
+ *b*.
Find *m
*and
*b*.

**Scroll
down for the solution.**

**8/15/2014
**Solution.**
**Since
the degree of the numerator in f(x) = x^{2}
/ (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 x^{2}
by (x + 1) to get:

f(x)
= (x – 1) + 1/x^{2}.

Now,
as *x* → ∞,
f(x) → x – 1.

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