Page 44 - Calc for the Clueless

-
+
Intercept (6,0). f(6 ) is negative. f(6 ) is negative. The picture is...
To summarize, if the exponent is even positive, the sketch does not cross at the intercept.

Example 13—

Intercept (2,0), f(2 ) is negative; f(2 ) is positive. The curve around (2,0) looks like...
+
-
Example 14—

Intercept (-4,0), f(-4 ) is positive; f(-4 ) is negative. Around (-4,0) the curve will look like...
-
+
To summarize, if the exponent is odd positive, the sketch will cross at the intercept:

Let's see what it will look like near the vertical asymptotes. We attack the problem in exactly the same way.

Example 15—

-
Vertical asymptotes at x = 4, f(4 ), f(4 ) are positive, and the curve near x = 4 looks like...
+
8
To reemphasize, f(4 ) = f(4.1)= 7/(4.1 -4) = 7/0.00000001 = 700,000,000, which is big. The curve tends to plus
+
infinity, from the right side of 4. Similarly, the curve goes to plus infinity from the left side.