MATH 100: Quiz 3

You may use a calculator on this quiz. You may not use a cell phone or computer. To receive full credit please show your work carefully and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next. There are questions on both sides of this quiz paper.
  1. (30 points) For the functions f(x) = 1/x and g(x) = (1/x)²:
    a) Find and simplify an equation for (f + g)(x).




      b) Find the domain of (f + g)(x).




      c) Find and simplify an equation for (f(g(x)).





  2. (20 points) Does the function described by the table below have an inverse function? Justify your answer.
    x -101234
    h(x) -2121-3-6





  3. (10 points) Find the inverse of the function f(x) = 4/x.





  4. (20 points) Give the equation of a third degree polynomial with zeros at -1 and 2. (There is more than one correct answer to this question.)





  5. (20 points) Find the equation of a parabola with vertex (3,4) and y-intercept (0, -5). (You may leave the equation in standard form.)








Bonus (5 points) The height y of a ball is y = -x² + 2x + 4, where x is the horizontal distance (in feet) from where the ball is thrown. What is the maximum height of the ball?