1. (a) Write an equation for the function that has the shape of f (a?) : {Vi but reected in the X-aXis, shifted left one unit, and then shifted up 2 units. (b) Find the inverse of the function f(:13) : 2 + V3 27, and state the domain and range of f'l. 2. For this problem, round all your answers to one decimal place. The distance (miles) a car can travel on one gallon of gas at speed v miles per hour is given by 4.8 M = 30 2 - v. (a) At 50 mph how far can the car travel on one gallon of gas? (b) Find the speed which maximizes fuel efficiency. (c) Find the largest value of M.3. The graph of a polynomial function p(x) is shown here. (a) Is the degree of this polynomial function even or odd? Explain how the graph indicates this. (b) Is the leading coefficient of the polynomial function positive or negative? Explain how the graph indicates this. (c) What is the value of the constant coefficient? Explain how the graph indicates this. (d) Identify the real zeros of the polynomial function, and state whether the multiplicity of each zero is even or odd. (e) Provide a possible function that could be represented by the graph. (Your answer will be checked by entering the function that you provide into a graphing tool and compared to the graph shown here.)2m2+m6 4. Suppose 1" is the rational function dened by x) : m. a: :r, (a) Find the coordinates of any holes in the graph of 1"(32). If there are none, state NONE. Please explain or show work to justify your answer. (b) Identify any vertical asymptotes in the graph of 713:). If there are none, state NONE. Please explain or show work to justify your answer. (0) Identify any horizontal asymptotes in the graph of ?\"(:E). If there are none, state NONE. Please explain or show work to justify your answer. (d) Determine the y-intercept of the graph of it). Please explain or show work to justify your answer. 5. Solve the following rational inequality and graph the solution set. Please explain or show work to justify your