Let fx x 8x 59x 88x Find the vertical asymptote Find the

Let f(x) = (x - 8)(x + 5)/(9x + 8)(8-x) Find the vertical asymptote. Find the horizontal asymptote. What graphical feature occurs at x = 8? (Select all that apply.) Vertical asymptote Hole Intercept

Solution

f(x) = (x-8)(x+5)/(9x+8)(8-x) = (x^2 -3x -40)/(-9x^2 + 64x + 64)

a) Vertical asysmptote ====> (9x+8)(8-x) = 0 ========> x = 8, -8/9

b) Horizontal asymptotes =======> -1/9

c) At x = 8 ====> Vertical asysmptote