Page 59 - Calc for the Clueless

Example 33—

x axis symmetry

For completeness, we will sketch a curve that is not a function of x or y.

Example 34—

Intercept is (0,0). It turns out to be an isolated point since for all x values between -1 and 1, except x = 0,

is negative, making y imaginary.

Vertical asymptotes: x = 1, x =-1. Horizontal asymptotes: If we could talk about a degree, the degree of the
bottom is 1 and the degree of the top is 1. Horizontal asymptote is . Symmetry with respect to x,y axes.
The sketch is as follows:

That's about it. You could write a whole book on curve sketching, a large book. I hope this gives you a solid
idea on how to sketch curves.

Sometimes, you might like to know about the curve without actually drawing the curve itself. What questions
may you ask? Well I'll tell you.

Example 35—