Question

which line is a horizontal asymptote of the graph of function r?
r(x) = \frac{x^2 + 6x + 9}{x^2 - 16}
\bigcirc y = -\frac{9}{16}
\bigcirc y = 0
\bigcirc y = 1
\bigcirc the graph has no horizontal asymptotes.

Explanation:

Step1: Identify degrees of numerator/denominator

The numerator $x^2+6x+9$ has degree 2, denominator $x^2-16$ has degree 2.

Step2: Apply horizontal asymptote rule

For rational functions with equal degrees, the horizontal asymptote is the ratio of leading coefficients: $\frac{1}{1}=1$.

Answer:

C. $y = 1$