00:01
To find asymptotes, we will first consider the points where our function fx is not defined.
00:09
So we know the function is not defined when denominator is 0.
00:14
So to find the points where function is not defined, we will first consider as this x square minus 1 equals to 0.
00:23
From where we get x square equals to 1, which implies x equals to plus minus 1.
00:30
Thus our vertical asymptotes are x equals to 1 and x equals to minus 1.
00:45
And for very large value of x in this function, if we put x as very large value, we will get fx tends to 0 when x is very large.
01:02
Thus horizontal asymptot is our x -axis is x -axis.
01:20
So here we got our vertical asymptotes which are x equals to 1 and x equals to minus 1 and our horizontal asymptote is x -axis.
01:28
Here in this graph you can see this is y -axis and this is x -axis which is our horizontal asymptote.
01:36
And here are two lines.
01:38
This line is x equals to 1 our vertical asymptote and this line is x equals to minus 1 which is our another vertical asymptote.
01:46
Now we have to check symmetry of our graph.
01:53
To find symmetry, we'll put f of minus x.
01:58
So here, in this function, we will put minus x in place of x.
02:06
So we get, which becomes minus of fx...