question find all horizontal asymptotes of the following function. f(x) = (6x - 21)/(2x + 6) answer one…
question find all horizontal asymptotes of the following function. f(x) = (6x - 21)/(2x + 6) answer one horizontal asymptote
Answer
Answer:
$y = 3$
Explanation:
Step1: Recall horizontal - asymptote rule
For a rational function $f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, if $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$.
Step2: Identify $n$, $m$, $a_n$ and $b_m$
In $f(x)=\frac{6x - 21}{2x+6}$, $n = 1$, $m = 1$, $a_1 = 6$, $b_1 = 2$.
Step3: Calculate the horizontal asymptote
$y=\frac{a_1}{b_1}=\frac{6}{2}=3$.