Please Help I have attached my reference work and questions. Provide clear handwritten solutions for just question #2 and #3.

For each question down below provide a solution with all necessary steps and answer: [. What kind of question are you solving? I[I. If you were to choose these questions on a test, why would you choose them? [TI. Make a short comment where students might make mistakes and strategies they should use to either avoid these mistakes, or to answer the problem in o1l Question 1 P TR Given the graph of g(x) in the form, g(x) = o a) Determine the equation of g(x) b) State the x-intercept, y-intercept, vertical asymptote, horizontal asymptote, and slant asymptote. (if any). )Asx = 2, f(x)=? d)Asx = 27, f(x)>? Question 2 In the magical world or wizards and witches, Harry Potter, creates a potent love potion. This potion is rumored to bind the hearts of those who drink it, but its effectiveness diminishes over time in a manner described by the function: y = 4_2x-4 + 3 Here, y represents the remaining effectiveness of the love potion in units of enchantment, and x denotes the number of hours since the potion was TN a) Determine the initial effectiveness of the potion, when it was first brewed. b) Calculate how much the effectiveness of the potion decreases every hour, given the exponential nature of its decay. ) Describe the transformations applied to the parent function y = 4" to obtain the functiony = 4 -* + 3 , ; .1 Determine the inverse function f ~(y) that expresses the number of hours x in terms of the remaining effectiveness y of the potion. @ ISu e} i Ne! Simplify log(x\" + 12x + 11) log(x 1) a) Find the inverse of the function, logf(x2 +12x+ 11) = log(x2 ) b) Analyze the similarities and differences of f(x) to f (x) c) Determine the x-intercepts (zeros), y-intercepts, Vertical Asymptote (VA), Horizontal Asymptote (HA), Restrictions, and discontinuity (holes) of the original function, if any. A polynomial function f (x) =- x - x + kx + 12 is given. 3 a) Determine the value of k if (x + 2) is a factor of f (x). [1] b) Find the roots of the polynomial function and rewrite in its factored form. [2] c) Determine the end behavior of the function. [1]\fReflective Response 1 > This question involves understanding and manipulating polynomial functions. Specifically, it requires determining a constant, finding roots, factoring the polynomial and analyzing the end behavior of the {0110 Missteps might occur while: Testing the possible rational roots Using synthetic division. Confusion might arise while students determine the end behavior especially for polynomials of higher degrees with negative leading ISR This question covers a range of important algebraic skills that are important to assess a student's grasp of polynomials, factoring, the significance of synthetic division and their graphical behaviors