1. The problem statement, all variables and given/known data Sketch the graphs of the following functions and show all asymptotes with a dotted line y = (2x - 6)/ (x2-5x+4) i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s) iv) Describe the behavior of the function as it approaches and leaves vertical asymptotes and/or point of discontinuity v) State the horizontal asymptote. vi) State the Domain and Range 2. Relevant equations 3. The attempt at a solution I hope my thread title is correct. First off I factored the function y = 2(x-3)/(x-4)(x-1) i) This gave me my vertical asymptotes: x = 4, x = 1 ii) Without any points of discontinuity then I don't have any restrictions or non-permissible values (I think) iii) X intercept 0 = (2x-6)/(x2-5x+4) (0)(x2-5x+4) = 2x-6 0 = 2x - 6 6 = 2x x = 3 (3,0) iii) Y intercept y = 2(0)-6/(0)2-5(0)+4 y = -6/4 y = -3/2 (0,-3/2) iv) I believe I can do this once I figure out my graph v) Horizontal Asymptote: y = 2 vi) D: x ≠ 4, 1 Now I tried finding my range but substituting my horizontal asymptote into the function 2 = (2x-6)/(x2-5x+4) 2x2-10x+8 = 2x-6 2x2-12x+14 = 0 Using quadratic equation I get 3±√2 Now when I put all this onto my graph I don't know where to draw the lines. I think I've placed all my lines where I should but something seems wrong.