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Advanced Functions Chapter 3 Assignment [70] 1 [12]State the domain, range, and show the parity of each. a(x) = 2x3+5x2 -2 b (x ) = 2x6 +2 c(x) = -3x5 +5x3 - x 2 Consider f (x) = x3 and g(x) = 2f(x - 1) +3. a) [1]Write g using exponential notation, instead of referring to f. b) [4]What point on g corresponds to the point (2,-8) on f? 3 [4 marks] If f(x) = -2x3 + x2 + 7x - 1 fill in the blanks below: a) As x - -co f(x) - c) As x - 1f(x) - b) As x - Of(x) - d) As x - co f (x) - 4 [7]Use a chart with 3 preceding and 3 following intervals to estimate the X Y m instantaneous rate of change, (iROC) of f (x) = -2x3 + x2 + 7x - 1 at x=3. Provide evidence in your chart to support that you are accurate with your estimate to within 0.1 of the actual iROC value. minst ~ 5 Create a "unique-to-you," (i.e. no copying) polynomial function in factored form so that: a) [4 marks] a(x) has exactly 3 real distinct roots and approaches co as x approaches -co b) [3 marks] b(x) has 2 coincidental roots, as well as exactly one other real root, and approaches -co as x approaches -co c) [2 marks] c(x) is a cubic that has exactly one real root, (i.e. two complex roots). d) [3 marks] d(x) is any polynomial function that decreases on exactly two intervals, and increases on exactly one interval. 6 [6 marks]Factor each fully a(x) = 27x3 -125 b(x) = 64x5 - 8x2 c(x) = 5x3 - 7