Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function g(x)=x-3. Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations. (5 points) Part B: Let h (x) be the piecewise defined function of h(x) = < all necessary calculations. (5 points) f(x) if X 0 Question 3 (Essay Worth 15 points) (01.03, 1.06, 1.08 HC) A piecewise function f (x) is defined by f(x) = 3x+1-2 for x1 7 for x>1 X Part A: Based on the graph of f(x), what is the range? (5 points) Part B: Determine the asymptotes of f (x). (5 points) Part C: Describe the end behavior of f (x). (5 points) Question 4 (Essay Worth 15 points) (01.07 HC) A function g(x) is defined by g(x) = log4(x 3) + 2. Part A: Graph the logarithmic function g(x) and determine the domain, range, and x-intercepts. Show all necessary calculations. (5 points) Part B: Determine the vertical and horizontal asymptotes of g(x). Show all necessary calculations. (5 points) Part C: Describe the interval(s) in which the graph of g(x) is positive. Determine the end behavior of g(x). (5 points) 0 Question 1 (Essay Worth 10 points) (01.02, 1.03, 1.04 HC) Let f (x) = x + 4x 2x 12x + 9, g(x) = x+2x-3 and (x) = -x +1 x + 2x-3 Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points) Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)