Which of the following statements are true of this rational function? check all of the boxes that apply. f(x)=(x+a)(x+b)/x^2+ax 1. there is a removable discontinuity at x = –b. 2. there is a vertical asymptote at x = 0. 3. there are no removable discontinuities. 4. there is a vertical asymptote at x = –a. 5. there is a removable discontinuity at x = –a

There is a vertical asymptote at x = 0.

There is a removable discontinuity at x = –a

Step-by-step explanation:

The given rational function is

We can rewrite the function by factoring the denominator as

Vertical asymptotes: Vertical asymptotes occurs where the denominator is zero.

Removal discontinuity: If we have some common factor in the ration function which can be canceled out then at that point, there would be a removal discontinuity. This is same as a hole in the graph.

In the given rational function, we have (x+a) is common in both numerator and denominator. Thus, the removal discontinuity is given by

x+a =0

x = -a

For vertical asymtotes:

x = 0

Therefore, 2 and 5 are correct options.