Question

Which of the following phrases best completes the definition of a vertical asymptote below?A vertical line that the graph of a function approaches _____.

A. but thenturns away from
B.and sometimes intersects
C.and always intersects
D.but never intersects

Answer 1

Option: D is the correct answer.

A vertical line that the graph of a function approaches D. but never intersects.

Explanation:

Vertical asymptote--

Vertical asymptotes are a straight vertical line of the equation, through which the function will reach very close to it but will never intersect that line.

For example :

In the function:

`y=(1)/(x-2)`

the vertical asymptote of the function is the straight line x=2

Since the function reaches very close to the line but does not intersect it.

Answer 2

The appropriate finish to the definition is ...

... D. but never intersects.

_____

In general, an asymptote is a line that is approached, but not crossed. (There are exceptions among rational functions.)