00:01
So question is to graph the quadratic function y equals to f of x.
00:04
So given the quadratic function, we need to find its reciprocal function and we need to identify if there is any vertical asymptote.
00:12
So vertical asymptote exists where the function is zero since we know when we take reciprocal, the zero where the function is zero it becomes infinity and when the function attains infinity it comes to zero.
00:26
Now try to achieve zero.
00:28
So it becomes zero and it tends to infinity.
00:32
So now let's look at it to the first graph here.
00:35
The function is tending to minus infinity.
00:38
And another thing that to be remembered before going there, that function sign does not changes.
00:43
That is if y is greater than zero for x greater than zero, it will remain as it is.
00:50
And if y is less than zero for x less than zero, it will remain as it is.
00:53
Now here we can see if x is greater than zero, y, is less than zero so after reciprocal also this condition will be justified so now if you see here that function approaches infinity at this point which is one and this point which is five okay so at one we are approaching infinity at five we are approaching infinity and function is not touching zero anywhere so we will not have this condition so function will not will not have asymptote.
01:34
So, only thing left is to grab the function.
01:38
So for this point, when we know when, let's say, the given function, y equals to f of x, so y is minus two for x of three.
01:51
And when we take reciprocal of this, what we get is that f of 1 by 3 is minus 1 by 2.
02:03
So this is what we are plotting and this is our y.
02:06
So y of 3 is this value.
02:10
So let's plot the diagram now.
02:12
So at this point it's tending to infinity...