hi! please help solve this practice test using advanced functions methods

_ .4 3 1. Determine the value of k such that when f(X) =X + kx - 3X - 5 is divided by X 3, the remainderis 10. 2. a) Graph the parent function = 2* and the transformed function defined by y==-2fQ3x-1)+4 b) State the impact of transformations on the domain and range, intervals of increase and decrease, and end behaviour c) State the equation of the transformed function. f(x)= M 3. Given a rational function, x=-3 find all the asymptotes, domain, range, x and y intercepts. Discuss the end behaviour and the behaviour close to the vertical asymptote. Show all your work algebraically 4. The following transformations are applied to f (x) = log; X reflection in the x-axis, horizontal compression by the factor of 2, horizontal shift by 2 units to the right, and vertical shift down by 3 units. Write the equation of the new function, and find the coordinates of the following points: (1,0), (3, 1), (9.2). 5. A box without a lid can be made from a sheet of cardboard measuring 60 cm by 40 cm by cutting congruent squares from the four corners and folding the sides up. If the volume of the 3 box has to be greater than 5508 cm sdetermine the possible range of the dimensions of the cut-out squares 60 e 6. Solve the following equation: COSJ'ZX + a\\QOSa't' +1=0 U=sXx=4n _ 2 7. Find the instantaneous rate of change for f (X) = 3x" 5x * 23 when x = -2. 8. The height, in metres, of a nail in a water wheel above the surface of the water, as a function of time, can be modelled by the function h(t) = 4 sin|~ (t li- 2.5 where t is the time in seconds. During what periods of time is the nail below the water in the first 24 seconds that the wheel is rotating? 9. The half-life of a radio-active element is 850 year. Suppose that we have a sample of mass of 25 mg. a) Find a function that models the mass, m, remaining after t years. b) How much of a sample will remain after 90 years? c) How long will it take to have only 6 mg of this sample