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

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)