Page 48 - Calc for the Clueless

7
We head to minus infinity at x = -3. (x + 3) is an odd power. So since one end is at minus infinity, the other is
at plus infinity. It goes down (we don't know how far) but never hits the x axis and heads back to plus infinity at
6
x = -6. Since (x + 6) is an even power, both ends are at plus infinity. The ends both go to y = 3/2, the horizontal
asymptote. The sketch can now be finished....

You should be getting better now. Let's try an oblique asymptote.

Example 21—

Since the degree of the top is 1 more than the bottom, we have an oblique asymptote. We need three forms of
the equation: the original, the factored, and the divided.

x intercept—top = 0 in the second form: (2,0). y intercept—x = 0, easiest found in the first form: (0,-4). Vertical
asymptote—first or second form: x = 1. Oblique asymptote—third form: y = x - 3 with remainder going to 0.

+
Again we look at the rightmost vertical asymptote or x intercept, in this case (2,0). f(2 ) (form 2) is positive. (x-
2) is an even power, so there is no crossing, heading up to plus infinity at x = 1. Since the power of x -1 (1) is
2
odd, the other end is at minus infinity. The sketch then goes through the point (0,-4) with both ends going to the
line y = x - 3. The sketch is...