Question

Consider the table representing a rational function.

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

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

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 $x=0$ and $x=4$ function is undefined.

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

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

Therefore, option D is the correct choice.