Question

question
find all horizontal asymptotes of the following function.
f(x)=\frac{2(x - 4)}{x + 5}
answer attempt 1 out of 2
one horizontal asymptote
no horizontal asymptotes
one horizontal asymptote
two horizontal asymptotes
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Explanation:

Step1: Analyze the degrees of numerator and denominator

The degree of the numerator \(2(x - 4)=2x-8\) is \(n = 1\), and the degree of the denominator \(x + 5\) is \(m=1\).

Step2: Use the rule for horizontal asymptotes when \(n=m\)

When \(n=m\) (where \(n\) is the degree of the numerator and \(m\) is the degree of the denominator), the horizontal asymptote is \(y=\frac{a_n}{b_m}\), where \(a_n\) is the leading coefficient of the numerator and \(b_m\) is the leading coefficient of the denominator.
For \(f(x)=\frac{2(x - 4)}{x + 5}=\frac{2x-8}{x + 5}\), \(a_n = 2\) and \(b_m=1\). So \(y=\frac{2}{1}=2\)

Answer:

One Horizontal Asymptote (\(y = 2\))