00:01
Okay, given this rational function, we know that we're looking at a domain of all real numbers.
00:06
However, x cannot be negative 1 or negative 5, because if we factor this out, we end up with 2x plus 1, divide by x plus 1 times x plus 5, which means if we have negative 1 or negative 5, we'd be dividing by 0, which is undefined.
00:21
So the domain is all real numbers except for x cannot equal negative 1 or negative 5.
00:24
Therefore, we know we have vertical asymptotes that x equals negative 1, x equals negative 5.
00:29
So vertical equals negative 1 comma x equals 5.
00:41
Given this, we also notice that we have a horizontal asymptote of y equals 0, because if we write the limit as x approaches, you have 2 plus 1 over x over x plus 6 plus 5 over x equals 0.
01:05
Y equals 0 is our horizontal asymptote.
01:12
Now, determining the x intercepts and y intercepts, we can see looking at this function, the f of x equals 0.
01:19
When you set 2x plus 1 over x plus 1 times x plus 5 equals to 0, you end up with x equals negative 1 1⁄2.
01:26
F equals 1 over 1 times 5, which is 1 over 5.
01:30
So the x intercept is negative 1⁄2, and the y intercept is 0, 1 .1 .5th...