1. Determine the type of symmetry, if any, in the following graphs. State whether the function is odd, even, or neither. a. 3 -3 -2 -1- -2 -31 b. - 2- y = f(x) -5 2. Algebraically determine the type of symmetry, if any, in the following functions. State whether the function is odd, even, or neither. 2 a. f(x) = 3x -x32 b. f(x) = vx+1 2 c. f(x) =-_ 3 b. f(x) = 2x -5 x+1 1 4. What combinations of vertical, horizontal, and oblique asymptotes are not possible for a rational function?5. Find the following characteristics of the graph of the function f(x) = 3x(x -5)'. 3 a. Critical point(s) 3 6. Find the absolute extrema for the function f(x) = x - &x -1 on the interval [1, 10]. 7. For the following graph of y = f(x), find where the function YFAX) (1 a. is increasing (1 b. is concave down 1 C. has inflection point(s)5 8. Given the function f(x) = 12 x 6 "- x' + x-1, find the intervals of concavity and the inflection points.1 9. Is the following statement true? Explain. If f' (2) = f" (2) = 0, then there must be a point of inflection at x = 2. (3) 10. Sketch a continuous curve for which each of the following statements is true. Label all key points with their corresponding coordinates on the actual graph. f(- 1) = 4, f(0) = 2, f(1) = 0 f(- 1) =f' (1) =0 f' (x) > 0 for the interval (- co, - 1) U (1, co) f (x) 0 for the interval (0, co)14 11. Follow the 8 Steps to Successful Curve Sketching to sketch the graphs of the X fox) =. Be sure to clearly label each of the 8 steps you have demonstrated in your work, starting with Step 1. Use the following pages to show your work. Summary domain y-intercept asymptotes symmetry intervals of increase and decrease and increasing: critical point(s) decreasing: CP: local extrema max: min: concavity and inflection point(s) down: up: IP