14. The rectangle below has a certain width and length. When the width is doubled and the length is tripled the new rectangle will have an area of 5544 cm and a perimeter of 310 cm. Determine the exact value of the / and w. Show a full solution. 1 15. Two numbers have a sum of M. Determine an expression for the two numbers that would have the largest possible product. Justify your answer algebraically and numerically. Verify that your answer works by choosing a value of M. 16. Write the equation of the transformed function, g(x), if f(x) = x has gone through the following transformations. g(x) =3/[-3(x +1)]+4 17. a) The graphs of f and g are shown below. Describe the sequence of transformations could be used to transform finto g. Show all steps - Explain your thinking. b) Write g in terms of f. Justify your choice. c) Write f in terms of g. Justify your choice. d) Write the equation of each function.18. a) Determine the equation of the quadratic function with zeros 8+513 and passing through the point (-1, -12). b) Write a quadratic equation that has roots x =2+ 13 . Verify your answer. c) Create a quadratic equation that has roots (solutions) x = 4 and x =1/2 . Express your answer in standard form. d) Determine the equation of a quadratic function with zeros 1+v5 and 1-v5 and passes through the point (2, 5) e) Write the equations of three more quadratic functions that are in the same family of functions as your answer to d).19. a) Solve the system of equations given by /(x)=-2(x-2) +2 and g(x)=--x+3. 9 What is the meaning of this solution? b) Solve the system: Q y=4(x-2)(x+5) Q y=-4x+44 c) Determine the equations of the lines with slope -5 that intersect /(x) =-7x -5x +4 once, twice and never