SOLVE COMPLETELY

Let f (x) = x4 + 4x3 - 2x2 - 12x + 9, g(x)= vx2 + 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)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) [f ( x) if x " Are there any breaks in the domain of h (x)? Explain why or why not. (5 points)3x-1 -4 for x 3 x2 -7x + 12 Part A: Graph the piecewise function f (x) and determine the range. (5 points) Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points) Part C: Describe the end behavior of f (x). (5 points)x3 - 9X for x 3 Part A: Graph the piecewise function g(x) and determine the domain. (5 points) Part B: Determine the x-intercepts of g(x). Show all necessary calculations. (5 points) Part C: Describe the interval(s) in which the graph of g(x) is positive. (5 points)