Lesson 1: Asymptotes
The usual features of a graph's sketch includes:
Asymptotes are imaginary boundary lines that affect the position and the shape of a graph. There are generally 3 types of asymptotes:
(A) Vertical asymptote: x = k
The vertical line x = k is a vertical asymptote if as .
Generally vertical asymptotes can be obtained from the values of x which makes the equation (or y) undefined.
Find the equation of the vertical asymptote(s) for each of the following graphs.
x = 3 is the vertical asymptote since is undefined at x = 3.
(B) Horizontal asymptote: y = b
The horizontal line y = b is a horizontal asymptote if as .
Find the equation of the horizontal asymptote(s) for each of the following graphs.
(C) Oblique asymptote: y = mx + c
The horizontal line y = b is an oblique asymptote if
Find the equation of the asymptotes and the graph of