a. find the slant asymptote of the graph of the rational function.\nb. follow the seven - step strategy and…

a. find the slant asymptote of the graph of the rational function.\nb. follow the seven - step strategy and use the slant asymptote to graph the rational function.\nf(x)=\\frac{x^{2}+2x - 8}{x - 4}\na. select the correct choice below and, if necessary, fill in the answer box to complete the choice.\na. the equation of the slant asymptote is y = x + 6.\n(type an equation.)\nb. there is no slant asymptote.\nb. to graph the function, first determine the symmetry of the graph of f. choose the correct answer below.\norigin symmetry\ny - axis symmetry\nneither y - axis symmetry nor origin symmetry\nwhat is the y - intercept? select the correct choice below and, if necessary, fill in the answer box to complete the choice.\na. the y - intercept is 2.\n(type an integer or a simplified fraction.)\nb. there is no y - intercept.\nwhat is/are the x - intercept(s)? select the correct choice below and, if necessary, fill in the answer box within your choice.\na. the x - intercept(s) is/are - 4,2.\n(type an integer or a simplified fraction. use a comma to separate answers if needed.)\nb. there are no x - intercepts.\nfind the vertical asymptote(s). select the correct choice below and, if necessary, fill in the answer box to complete the choice.\na. the equation of the vertical asymptote is
Answer
Explanation:
Step1: Find vertical asymptote
For a rational function (f(x)=\frac{N(x)}{D(x)}), vertical asymptotes occur at the values of (x) that make (D(x) = 0). Given (f(x)=\frac{x^{2}+2x - 8}{x - 4}), set (D(x)=x - 4=0).
Step2: Solve for (x)
(x-4 = 0) gives (x = 4).
Answer:
A. The equation of the vertical asymptote is (x = 4)