Question

Consider the function…….. Identify all vertical asymptotes (select all that apply)Option E is hidden, it says 2.

Answer 1

Given the function below;

$f(x)=\frac{(x-2)^2(x+1)(x+3)}{x^3(x+3)(x-4)}$

Note that: The vertical asymptote(s) is (are) determined where the denominator equals zero. That is, where the function is undefined. Hence, we would solve it by setting the denominator equal to zero as follows;

$\begin{gathered} x^3(x+3)(x-4)=0_{} \\ \text{This means;} \\ x^3=0 \\ x+3=0 \\ \text{And,} \\ x-4=0 \\ \text{Therefore, } \\ x=0,x=-3,x=4 \end{gathered}$

ANSWER:

The vertical asymptotes are identified as;

$0,4\text{ and -3}$

Options (a), (c) and (d) are correct