Page 41 - Calc for the Clueless

(x-3)(x+1)=0. Intercepts are (3,0) and (-1,0).

Example 3—

Intercepts are (0,0), (1,0), and (2,0).

y intercepts. Just like the line, y intercept means a point where x = 0.

Example 4—

Substitute x=0.

. y intercept is (0,8).

Example 5—

For x = 0, we get -3/0. There is no y intercept.

Warnings:

1. If you get the sign of the y intercept wrong, you will never, never sketch the curve properly.

2. Functions have one y intercept at most (one or none).

3. If we have the intercept (0,0), it is one of the x intercepts, maybe the only one, but the only y intercept. We
do not have to waste time trying to find another one!

Vertical Asymptotes

A rational function has a vertical asymptote whenever the bottom of the fraction is equal to 0.

Example 6—

Asymptotes are vertical lines x = 0, x = 4, and x = -3.

Two more definitions need to be reviewed before we move on.

Note
Suice polynomials have no denominators, they have no vertical asymptotes. As we will see, they
have no asymptotes at all.