Q25. - Algebra 1

Question

Identify the asymptotes of each function.

$y=\frac{2}{\left(x-4\right)\left(x+2\right)}$

Step-by-Step Solution

Answer

The asymptotes of the given function are $x=4$, $x=-2$ and $y=0$.

Step 1. Define asymptotes.

An asymptote is a line that the graph of a function approaches.

Step 2. Set a denominator equal to zero.

Set a denominator of a given expression equal to zero.

$\left(x-4\right)\left(x+2\right)=0$

Step 3. Simplify.

Simplify the above expression.

$\begin{array}{l}\left(x-4\right)=0\text{ or }\left(x+2\right)=0\\ x=4x=-2\end{array}$

Therefore, the vertical asymptotes are $x=4$ and $x=-2$. Horizontal asymptotes are $y=0$.