00:01
Here we have y is equal to 2x plus 3 divided by x squared minus x minus 20.
00:12
And the denominator there we can factor as x minus 5 times x plus 4.
00:27
So this then has x -intercept at y is equal to, well, x -intercept means that my y is 0.
00:51
So that means that 0 is equal to 2x plus 3 divided by x minus 5 over x plus 4.
01:02
And the denominator cannot be 0, so that means that 2x plus 3 must be 0, or x is negative 3 over 2.
01:13
So the y -intercept is the point negative 3 over 2, 0.
01:18
And then your y -intercept is going to be at x is 0, so there your y then is equal to 2 times 0 plus 3 divided by 0 minus 5 times 0 plus 4.
01:45
And that is equal to 3 divided by negative 20.
01:51
So your y intercepted is at 0 and negative 3 over 20.
01:56
And we will have vertical asymptotes where the denominator is 0, so where x minus 5 times x plus 4 is 0, so at x is 5, and at x is negative 4.
02:19
So these are your vertical asymptotes.
02:22
And let's see here if i empty graph this that is going to look like 2x plus 3 divided by x squared minus x minus 20 and we have horizontal asymptotes at let's see what happens at the end behavior.
03:49
Okay, so as x goes to positive infinity, then the leading coefficients of our function, which are 2x over x squared, that goes to, let's see, i can cancel the x, so this then is, so your n behavior model is 2x over x squared, which is 2 over x.
04:33
So then that goes to 0...