Page 45 - Calc for the Clueless

Example 16—

Vertical asymptote at x = 3. f(3 ) and f(3 ) are negative. The curve near x = 3 looks like...
-
+
To summarize, if the exponent is even positive in the denominator, near the vertical asymptote, both ends go to
either plus infinity or minus infinity.

Example 17—

+
Asymptote x = -6. f(-6 ) is negative; f(-6 ) is positive. The curve is...
-
Example 18—

Exponent is 1 (odd). Asymptote x = 5. f(5 ) is positive; f(5 ) is negative. The curve near x = 5 is...
-
+
To summarize, if the exponent is odd positive in the denominator, on one side of the asymptote the curve goes
to plus infinity and on the other the curve goes to minus infinity.

We are now ready to put all the pieces together. With some study and a little practice, you positively will be
able to sketch curves with intercepts and asymptotes only in under two minutes!!!!!!!

Example 19—

First locate the intercepts. x intercept means y = 0 means top of fraction = 0. (2,0) and (-1,0). y intercept, the
only long part. Substitute x = 0.