Question #4797

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)

Expert's answer

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’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’t asymptotes because there function is continuous.

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

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’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’t asymptotes because there function is continuous.

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

## Comments

## Leave a comment