00:01
Nitro, it looks like you need some help on this function.
00:02
And first of all, you want to know what the domain is.
00:06
And so the domain is going to be all real numbers except for 1.
00:11
You cannot place 1 in there.
00:13
So it's going to be x such that x cannot be equal to 1.
00:22
If you need that in interval notation, you would have negative 1 to 1, and then that's a closed parenthesis, united with 1 to positive infinity.
00:34
Now, next you need to list all the vertical asymptotes and so on.
00:38
So we have our vertical asymptote, first of all, is the value that makes the denominator 0.
00:44
So that's the equation x equals 1.
00:47
Your horizontal asymptote is the limiting value.
00:51
It's the value that this graph approaches.
00:53
And that as x goes to infinity or negative so plus or minus infinity this is going to get closer and closer to zero so y equals zero is your horizontal asymptote now you don't have an oblique asymptote there is none holes there are no holes there are none then you have to list the x and y intercepts so we know that the x -intercept if we're dealing with the x -intercept the x -intercept occurs what x causes y to be zero and we know that there can't be a y of zero because that's where our asymptote is so there is none there is not an x intercept but our y intercept will occur when we plug zero in place of x and that that will be that corresponding y -intercept will be that point.
01:55
And so when we plug 0 into that function, we have that 2 over 0 minus 1.
02:04
So that will be a negative 2.
02:07
Now, that's going to depend on how some people will say.
02:10
I say the intercept is just negative 2.
02:13
Some people want it as a coordinate.
02:15
So you follow what your teacher is having you do.
02:18
Now next you want to tell whether this is one -to -one.
02:22
And the answer is yes, it is a one -to -one function.
02:26
Each x has an individual y, so each x is only paired to one y value, and each y value is also only paired to one x value.
02:38
And then you need to find the inverse, and you want the inverse of the function to be written in a form like this.
02:46
So we take our original function, and you probably are taught to switch your x and y around...