Question

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.

Answer 1

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

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.