I- Let ƒ be the function defined by: f(x) = x²+9 x+2 1) Determine the domain of definition Df of f. 2) Calculate the limits off at the open boundaries of De, deduce an asymptote to the curve (C) of f. (3) a) Calculate f'(x) and show that f is strictly decreasing on each interval of its domain of definition. b) set up the table of variation of f. 1) 4) a) Calculate the real numbers a, b and c such that f(x) = ax + b + x + 2² b) Deduce the equation of an asymptote to (C). C) study the relative position ic) +12) 5) Calculate the coordinates of the points of intersection between (C) off and the coordinates' axis. 6) Determine the equation of the tangent to (C) at the point A of abscissa 2. 7) C Draw (C).