Problem#10: (Section 2.6) f(x)= (x2 -4x +3)(x-7) 1 PM" ' (X-7)(X+l) 2 Us! the procedure below and show all work. Slap 6 (drawing the graph ofxs optlanw Strategy for Grnphing a Rnonnl Function The following strategy can be used to graph f (X) = pg;- q x where p and q are polynomial functions with no common factors. 1. Determine whether the graph of f has symmetry. f (x) = f (x) y-axis symmetry f(.\\') = f (x) origin symmetry 2. Find the y-intcrcept (if there is one) by evaluating 1(0). 3. Find the x~intercepts (if there are any) by solving the equation p(x) = 0. 4. Find any vertical asymptote(s) by solving the equation q(x) : 0. 5. Find the horizontal asymptote (if there is one) using the rule for determining the horizontal asymptote of a rational function 6. Plot at least one point between and beyond each x-intereept and vertical asymptote Problem#8: (Sections 2.4, 2.5) 10 Points Given : 6x3+ 11x2 - 92x + 15 = 0 a) Use the Descrates' Rule of signs to determine possible number of positive and negative real roots. b) List all possible rational roots c ) Given that one of the zeros is x-3, Use synthetic division to factor the original polynomial. d ) Find the remaining roots of the given polynomial. Problem#9: : 1+4 (Section 2.7) 53 10 points Solve rational inequality. 2.x-1Problem#7: (Section 2.3. 1.3) Given : f(x) = -6x3(x + 1)(x + 4)2 10 points Follow steps 1-5 below to graph f(x) A Strategy for Graphing Polynomial Functions Graphing a Polynomial Function f(x) = and" + an-1 1"- + an-21" -2 + .. . + ajx + do, an # 0 1. Use the Leading Coefficient Test to determine the graph's end behavior. 2. Find .x-intercepts by setting f(x) = 0 and solving the resulting polynomial equation. If there is an x-intercept at r as a result of (x - r) in the complete factorization of f(x), then a. If k is even, the graph touches the x-axis at r and turns around. b. If k is odd, the graph crosses the x-axis at r. c. If k > 1, the graph flattens out near (r. 0). 3. Find the y-intercept by computing f(0). 4. Use symmetry, if applicable, to help draw the graph: a. y-axis symmetry: f(-x) = f(x) b. Origin symmetry: f(-x) = -f(x). 5. Use the fact that the maximum number of turning points of the graph is n - 1, where n is the degree of the polynomial function, to check whether it is drawn correctly.Problem#6: f(X) : '_7_____ (Section 1.8) 3x 1 Find equation for the f"(x). Then check if your answer is correct by evaluating f(f_1(x)) MM 4) Divide complex numbers: (section 2.1) 2+7i 72i 5) Use Function Tramfonnation rules to graph f(x)= '/2 [x 7 11+2. Name the elementary function to start with and describe each transformation step by step. Then sketch the graph after each step Plot FINAL graph off/x) in the grid below (Section 1.6)