Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \) \( f(x)=\frac{x^{2}+9 x+18}{x^{2}+6 x+9} \) Find any vertical asymptotes of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, (Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \) and the rightmost asymptote is (Type equations.) C. There are no vertical asymptotes.

To find the vertical asymptotes of the function \( f(x)=\frac{x^{2}+9 x+18}{x^{2}+6 x+9} \), we first need to identify where the denominator is equal to zero. The denominator can be factored as: \[ x^{2}+6 x+9 = (x+3)(x+3) = (x+3)^{2} \] Setting this equal to zero, we find: \[ (x+3)^{2} = 0 \implies x = -3 \] Since the function is undefined at \( x = -3 \), this indicates that there is a vertical asymptote at this point. The correct answer is: A. The function has one vertical asymptote, \( x = -3 \). Regarding the graph, you can visualize it by plotting the function around \( x = -3 \) and observing its behavior. As \( x \) approaches -3 from the left, \( f(x) \) goes to \( +\infty \), and as \( x \) approaches -3 from the right, \( f(x) \) goes to \( -\infty \), confirming the vertical asymptote there!