Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

True or False If $x=3$ is a vertical asymptote of a rational function $R$, then $\underset{x\to 3}{\lim }\left|R\left(x\right)\right|=\infty$.

Step-by-Step Solution

Answer

The statement is true.

Step 1. Concept Used

It is known that as $x$ approaches some number $c$, the values of $\left|R\left(x\right)\right|\to \infty$, then the line $x=c$ is a vertical asymptote of the graph of $R$.

Step 2. Check whether the statement is true

The notation $\underset{x\to 3}{\lim }\left|R\left(x\right)\right|=\infty$ can be read as $x$ tends to $3$ the value of $R\left(x\right)$ tends to $\infty$.

So using the above information it can be said that the line $x=3$ is a vertical asymptote of the rational function $R$.

So the given statement is true.