Why is the vertical asymptote for #f(x)=sqrt((x-3)/x)# x=0 when the domain is (-infinity,0)#uu#(3,+infintiy)?
I need to find the asymptote for this function but I don't understand why the answer is x=0.
Our teacher told us to calculate lateral limits for, in this case, 0 and 3 and find if either is infinite as x approaches from right and left. But if that's the case then what happens when calculating the limits for x approaches 3 is it undefined?
I need to find the asymptote for this function but I don't understand why the answer is x=0.
Our teacher told us to calculate lateral limits for, in this case, 0 and 3 and find if either is infinite as x approaches from right and left. But if that's the case then what happens when calculating the limits for x approaches 3 is it undefined?
1 Answer
See below.
Explanation:
Vertical asymptotes occur where the function is undefined. In this case at
If we take the left and right limits as x approaches zero:
? This confirms an asymptote at
as
If we plug
So the function is defined at
This is one of those cases where if we solve the limit by plugging in
But we can see from the graph, that the left limit does not exist, as well as trying a value to the left of
This is the square root of a negative number.
So the domain should be:
Note the inclusion of
graph{y=sqrt((x-3)/x) [-12.66, 12.65, -6.33, 6.33]}
In the question you are asking why the asymptote is
Remember that an asymptote is a line that a curve approaches, it never reaches it. The