Hello I need some help with these questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. Use calculus and algebraic methods to do a complete analysis (i.e. domain and range, intercepts, critical points, intervals of increase and decrease, points of inflection, intervals of concavity, local maximum or minimum points) for each of the following functions and then sketch the graph of the function. You can use graphing software (Desmos) to verify your analysis and graph. Keep in mind that your analysis is the most important aspect of this question, not the graph. a. f (X) = -x2 + 4x - 3 b. g(x) = x3 - 6x2 + 9x c. h(x) = x4 - 6x2 d. p(x) = 3sin(2x) (rely on DESMOS and your trigonometric skills from MHF4U e. q(x) = -2 (x +3)2 determine and use the asymptotes