follow the seven step strategy to graph the following rational function.\n\nf(x)=\\frac{x…

follow the seven step strategy to graph the following rational function.\n\nf(x)=\\frac{x - 6}{x^{2}-36}\n\nwhat is/are the x - intercept(s)? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the x - intercept(s) is/are\n(type an integer or a simplified fraction. use a comma to separate answers as needed.)\nb. there is no x - intercept.\n\nfind the vertical asymptote(s) or hole(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. there is no vertical asymptote, but the graph has hole(s) at x=\n(use a comma to separate answers as needed.)\nb. the equation(s) of the vertical asymptote(s) is/are and the graph has no hole(s).\n(type an equation for the asymptote. use a comma to separate answers as needed.)\nc. the equation(s) of the vertical asymptote(s) is/are x = - 6 and the graph has hole(s) at x = 6.\n(type an equation for the asymptote. use a comma to separate answers as needed.)\nd. there is no vertical asymptote and there is no hole.\n\nfind the horizontal asymptote(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the equation(s) of the horizontal asymptote(s) is/are y = 0.\n(type an equation. use a comma to separate answers as needed.)\nb. there is no horizontal asymptote.\n\nplot points between and beyond each x - intercept and vertical asymptote. find the value of the function at the given value of x.\n\nx - 9 - 8 5 7 8\nf(x)=\\frac{x - 6}{x^{2}-36}-\\frac{1}{3} 5 \\frac{1}{13} \\frac{1}{14}\n(simplify your answers.)

follow the seven step strategy to graph the following rational function.\n\nf(x)=\\frac{x - 6}{x^{2}-36}\n\nwhat is/are the x - intercept(s)? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the x - intercept(s) is/are\n(type an integer or a simplified fraction. use a comma to separate answers as needed.)\nb. there is no x - intercept.\n\nfind the vertical asymptote(s) or hole(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. there is no vertical asymptote, but the graph has hole(s) at x=\n(use a comma to separate answers as needed.)\nb. the equation(s) of the vertical asymptote(s) is/are and the graph has no hole(s).\n(type an equation for the asymptote. use a comma to separate answers as needed.)\nc. the equation(s) of the vertical asymptote(s) is/are x = - 6 and the graph has hole(s) at x = 6.\n(type an equation for the asymptote. use a comma to separate answers as needed.)\nd. there is no vertical asymptote and there is no hole.\n\nfind the horizontal asymptote(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the equation(s) of the horizontal asymptote(s) is/are y = 0.\n(type an equation. use a comma to separate answers as needed.)\nb. there is no horizontal asymptote.\n\nplot points between and beyond each x - intercept and vertical asymptote. find the value of the function at the given value of x.\n\nx - 9 - 8 5 7 8\nf(x)=\\frac{x - 6}{x^{2}-36}-\\frac{1}{3} 5 \\frac{1}{13} \\frac{1}{14}\n(simplify your answers.)

Answer

Explanation:

Step1: Substitute (x = 7) into (f(x)=\frac{x - 6}{x^{2}-36})

First, simplify the denominator (x^{2}-36=(x + 6)(x - 6)) (using the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)), here (a=x) and (b = 6)). Then (f(x)=\frac{x - 6}{(x + 6)(x - 6)}=\frac{1}{x + 6}) for (x\neq6)

Step2: Calculate (f(7))

Substitute (x = 7) into (f(x)=\frac{1}{x + 6}). We get (f(7)=\frac{1}{7+6})

Answer:

(\frac{1}{13})