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. \[ f(x)=\frac{x^{2}+2 x-8}{x-4} \] a. Select the correct choice below and, it necessary, till in the answer box to complete the choice. A. The equation of the slant asymptote is $y=x+6$ (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 What is the $y$-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete the choice. A. The $y$-intercept is (Type an integer or a simplified fraction.) B. There is no $y$-intercept.
Solution
Step 1 ：The question is asking for the slant asymptote of the given rational function. A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 1, so there is a slant asymptote.
Step 2 ：To find the slant asymptote, we can perform polynomial division. The quotient of the division will be the equation of the slant asymptote.
Step 3 ：After finding the slant asymptote, we can find the y-intercept of the function by setting x to 0 in the function.
Step 4 ：The slant asymptote of the function is \(y = x\) and the y-intercept is 2.
Step 5 ：Final Answer: The equation of the slant asymptote is \(\boxed{y = x}\) and the y-intercept is \(\boxed{2}\).
