Answer to Question #4797 in Calculus for adriana

Question

consider the function F=
x^2 | x+2| for x<-2
(2/x)+1 for -2 <or= x < 0
3 for x=o
(sinx/x) for x>0

describe all asymptotes of F (vertical and horizontal)

Answer 1

Asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.We have function


The line x=a is a vertical asymptote of the function if at least one of the following statements is true:

Function is defined everywhere except x=0
Let&rsquo;s find limit

Therefore we have the vertical asymptote x=0
Horizontal asymptotes are horizontal lines that the graph of the function approaches as


Therefore we have the horizontal asymptote y=1
When a linear asymptote is not parallel to the x- or y-axis, it is called an oblique asymptote or slant asymptote.
A function f(x) is asymptotic to the straight line

if

Under the function schedule we see that others asymptotes are not present.
In other points it isn&rsquo;t asymptotes because there function is continuous.

We have two asymtotes x=0(vertical) and y=1(horizontal).