Question

find all horizontal asymptotes of the following function.

f(x)=\frac{2 x^{2}-14 x-16}{3 x+18}

answer attempt 1 out of 2

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator \(2x^{2}-14x - 16\) is \(n = 2\) (the highest power of \(x\) is \(x^{2}\)). The degree of the denominator \(3x + 18\) is \(m=1\) (the highest power of \(x\) is \(x\)).

Step2: Apply the rule for horizontal asymptotes

If \(n>m\) (where \(n\) is the degree of the numerator and \(m\) is the degree of the denominator), then there is no horizontal asymptote. Here \(n = 2\) and \(m = 1\), and \(2>1\).

Answer:

No Horizontal Asymptotes