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.

Using the asymptote concept, the correct option is:

In this problem:

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

A similar problem is given at link

The function has a hole when and a vertical asymptote when   .

Step-by-step explanation:

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 and function is undefined.

We can also see that that the value of function to the left of 0 is and the value of function to the right of 0 is . This means that function has a point discontinuity that is at is zero for both numerator and denominator. Therefore, the function has hole at .

Upon looking at table we can see the value of function to the left of 4 is and the value of function to the right of 4 is . This means that function is approaching to different directions around . Therefore, the function has a vertical asymptote at .

Therefore, option D is the correct choice.

whatvare the choices

step-by-step explanation: