Consider the curve y = f(x) where f is the rational function defined by f(x) =...

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Consider the curve y = f(x) where f is the rational function defined by f(x) = x-2 a) Calculate the coordinates of the y-intercept of the curve. b) Show that the curve has no x-intercepts. c) Express f(x) in asymptote form, i.e. f(x) = Q(x) + R(x) D(x) = d) Determine the equations of the two asymptotes of the curve y f(x). For each asymptote, state whether it is a horizontal, vertical, slant or curve asymptote. (2 marks) e) Determine the coordinates of the two critical points of the curve. f) Sketch the curve and its asymptotes on the same set of axes. Include in your sketch the coordinates of the y-intercept and the two critical points. (3 marks) Consider the curve y = f(x) where f is the rational function defined by f(x) = x-2 a) Calculate the coordinates of the y-intercept of the curve. b) Show that the curve has no x-intercepts. c) Express f(x) in asymptote form, i.e. f(x) = Q(x) + R(x) D(x) = d) Determine the equations of the two asymptotes of the curve y f(x). For each asymptote, state whether it is a horizontal, vertical, slant or curve asymptote. (2 marks) e) Determine the coordinates of the two critical points of the curve. f) Sketch the curve and its asymptotes on the same set of axes. Include in your sketch the coordinates of the y-intercept and the two critical points. (3 marks)