00:01
This time, they give us the rational function, r of x, is equal to 4x squared over x squared minus 2x minus 3.
00:14
Let's write in that x squared.
00:15
Make sure i get something.
00:16
Okay.
00:18
Let's change this form to give us a bit more information for x squared over x minus 3, x plus 1.
00:27
That should do the trick.
00:28
Foil it out you end up with x squared minus 3x plus x that's minus 2x and then a minus 3 when you do the last terms looks good okay what does this tell us we have an x intercept at zero and multiplicity too so it will just bounce off the x -axis what else do we know let's look for our y intercept we'll put zero in there we will end up with a zero zero right so it has the y and x intercept at zero zero now what about asthmatotes vertical asymptotes at 3 and negative 1 thanks to that denominator factors what about the horizontal asymptote according to the section we look at the leading terms since the polynomials are of the same degree divide their coefficients 4 over 1 that's just 4 now we have enough information to start graphing our rational function okay let's make sure we got those asymptotes in there we have one at negative one.
01:33
And one at three, two, three, three.
01:44
Don't forget our horizontal asymptote.
01:46
One, two, three.
01:53
Maybe i drew it too high up.
01:55
You can work with that.
01:56
Okay.
01:58
We also have that intercept at zero, comma, zero.
02:04
Okay, that's look at our graph in reason.
02:06
The top is always going to be positive.
02:08
What about this? when we're ai way out at infinity, we will have a number very close to four...