Question

question
find the horizontal asymptote. give your answer in the form ( y = b ), or enter ( varnothing ) if there is none.
f(x)=\frac{1}{5 - x}
provide your answer below:

Explanation:

Step1: Recall the rule for horizontal asymptote of rational functions

For a rational function \( f(x)=\frac{a}{bx + c}\) (where \(a,b,c\) are constants and \(b
eq0\)), we find the limit as \(x\to\pm\infty\).

Step2: Calculate \(\lim_{x\to\infty}\frac{1}{5 - x}\)

As \(x\to\infty\), \(5-x\to-\infty\). So \(\lim_{x\to\infty}\frac{1}{5 - x}=0\).

Step3: Calculate \(\lim_{x\to-\infty}\frac{1}{5 - x}\)

As \(x\to-\infty\), \(5-x\to\infty\). So \(\lim_{x\to-\infty}\frac{1}{5 - x}=0\).

Answer:

\(y = 0\)