Problem
a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. \[ f(x)=\frac{x^{2}+2 x-24}{x-6} \] a. Select the correct choice below and, if necessary, fill in the answer box to complete the choice. A. The equation of the slant asymptote is $y=x+8$. (Type an equation.) B. There is no slant asymptote. b. To graph the function, first determine the symmetry of the graph of $\mathrm{f}$. Choose the correct answer below. origin symmetry neither $y$-axis symmetry nor origin symmetry y-axis symmetry
Solution
Step 1 ：Perform polynomial division on the numerator and denominator of the function. In this case, divide \(x^{2}+2x-24\) by \(x-6\).
Step 2 ：The quotient of this division will be the equation of the slant asymptote.
Step 3 ：The quotient of the division is \(x + 8\), which is the equation of the slant asymptote.
Step 4 ：Final Answer: \(\boxed{y = x + 8}\)
