Consider the table representing a rational function.

Which statement describes the graph of the function?

The function has holes when x = 0 and x = 4.
The function has vertical asymptotes when x = 0 and x = 4.
The function has a vertical asymptote when x = 0 and a hole when x = 4.
The function has a hole when x = 0 and a vertical asymptote when x = 4.

We have been given a table that represents values of a rational function. We are asked to choose the statement that describes the graph of the function.

We can see from our given table that at [tex]x=0[/tex] and [tex]x=4[/tex] function is undefined.

We can also see that that the value of function to the left of 0 is [tex]-0.244[/tex] and the value of function to the right of 0 is [tex]-0.256[/tex]. This means that function has a point discontinuity that is at [tex]x=0[/tex] is zero for both numerator and denominator. Therefore, the function has hole at [tex]x=0[/tex].

Upon looking at table we can see the value of function to the left of 4 is [tex]-100[/tex] and the value of function to the right of 4 is [tex]100[/tex]. This means that function is approaching to different directions around [tex]x=4[/tex]. Therefore, the function has a vertical asymptote at [tex]x=4[/tex].

Therefore, option D is the correct choice.

joaobezerra joaobezerra · Answer 2 · 2021-10-11T15:22:37+02:00

Using the asymptote concept, the correct option is:

The function has vertical asymptotes when x = 0 and x = 4.

A vertical asymptote is a point outside the function's domain, that is, a value of x for which the function is undefined.

In this problem:

According to the table, the function is undefined for x = 0 and x = 4.
Thus, these values are vertical asymptotes, and the correct option is:

The function has vertical asymptotes when x = 0 and x = 4.

A similar problem is given at https://brainly.com/question/23535769