Follow the instructions below to answer the questions.

(3) Let r(x) = 1 31 4 be a rational function. (a) State the domain, x- and y-intercepts of the graph y = r(x) (b) Find the vertical, horizontal, and/or slant asymptotes (if any) and determine the asymptotic behavior of the graph y = r(x) on each side of every vertical asymptotes (c) Find the values of y = r(x) when x = -6, -4, -2, -0.5, 1, 2, 5, 6 (d) Sketch the graph y = r(x) using the above information. (4) Let f(x) = (3)", g(x) = f-1(x) = log, x, and h(x) = 3 - log: (x -2). On the same ry-plane, sketch the graphs of the three functions by the following steps. (a) graph of f(x) = (3) by plotting points (b) sketch the graphs of g(x) = f-1(x) = log; a by an appropriate reflection of y = f(x). (c) using transformations of y = g(x) to sketch the graph of h(x) = 3 -log; (x - 2) and state the transformations used. (d) Find the domain, range and asymptote for each of the three functions. (5) Let q(x) = -x2+ 2x + 8 be a quadratic function. (a) Find the vertex and axis of symmetry of the parabola y = q(x) by completing the square (b) Find the x- and y-intercepts of the parabola (c) Sketch the graph of y = q(x) (d) State the domain and range of the quadratic function, and the intervals on which y = q(x) is increasing, decreasing g (e) State how to obtain the graph of y = q(x) using the transformation of y = x