Question

find the equation of any horizontal asymptote.
$f(x)=\frac{x^{2}+2x - 2}{x - 2}$
a. $y = 2$
b. $y = -2$
c. $y = 5$
d. none

Explanation:

Step1: Recall the rules for horizontal asymptotes

For a rational function \(f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}\), if \(n>m\), there is no horizontal asymptote. Here, the degree of the numerator \(n = 2\) (since the highest - power term in \(x^{2}+2x - 2\) is \(x^{2}\)) and the degree of the denominator \(m = 1\) (since the highest - power term in \(x - 2\) is \(x\)).

Answer:

D. None