Question

consider the following equation. name the vertical asymptote(s). f(x)=\frac{x^{3}+4}{4x^{3}-4x - 8}

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero. Set the denominator equal to zero: $x^{2}+4 = 0$.

Step2: Solve the denominator equation

For the equation $x^{2}+4 = 0$, we can rewrite it as $x^{2}=-4$. In the real - number system, there are no real solutions since the square of any real number $x$, $x^{2}\geq0$ for all real $x$.

Answer:

There are no vertical asymptotes in the real - number system.