why is there an open circle (1 Viewer)

[anonymoushehe]

why do they put an open circle I thought the asymptote indicates that the function is already not defined when x = 4, so should it not just be an arrow instead

 

[tywebb]

If you only include real numbers, as f(x) approaches , then 1/f(x) approaches 0 but does not reach it, hence the open circle at (4,0).

 

[anonymoushehe]

If you only include real numbers, as f(x) approaches , then 1/f(x) approaches 0 but does not reach it, hence the open circle at (4,0).

i get the first bit but im still confused about the open circle. i understand that the recipricoal function wont reach a value of 0 for that part, but is that not indicated by the asymptote in the graph?

 

[Average Boreduser]

i get the first bit but im still confused about the open circle. i understand that the recipricoal function wont reach a value of 0 for that part, but is that not indicated by the asymptote in the graph?

that asymptote is for the original function not the reciprocated one.

 

[anonymoushehe]

that asymptote is for the original function not the reciprocated one.

OHHHHHH wait that makes so much sense omg

 

[Rising Tide]

so f(x) is going to infinity but does not hit infinity when x approaches 4, doing the repricoal means that x approaches zero, but it does not hit zero, so thats why you have the open circle