00:01
All right, we have a function here.
00:03
We have a rational function, and our rational function is 4 plus x over x times x plus 2.
00:12
So we have f of x, and it's equal to 4 plus x over x times x plus 2.
00:22
Now we need to find all the values of x, x equal a, where our function is discontinuous.
00:28
And for each value of x, give the limit of the function as x approaches a, and then be sure to note where it doesn't exist.
00:36
So there's several parts here.
00:39
So the function is discontinuous at the two values x equal.
00:45
Well, where it's going to be discontinuous is where the function is undefined.
00:51
And so in our case, we have these, you know, down here in our denominator, what values will make our denominator equal to zero because that makes our function undefined.
01:03
So you can probably just look and tell, but just in case if we have x, it's already factored for us.
01:11
You take each one of those factors and set it equal to zero and then solve for x.
01:18
And so here we get x equals zero and x equal negative two.
01:22
And those are our two values that our function is undefined.
01:26
And you can kind of hopefully see in the graph here that at x equal negative 2 we get this vertical asymptote and also at x equals 0 which is our y axis that gives us a vertical asymptote the function is discontinuous at the single value uh let's see select the choice below and if necessary fill in the answer um okay so definitely a a is true a is discontinuous at the two values and these are a two values and these are two values where it's discontinuous...