Please answer the following question:

1. Factor fully the polynomial function: g(x) = 30x353x2+31x6 For the function state: - the x-intercept(s) (you need to factor the functions) - the y-intercept - the end behaviour ~ any symmetry the number of turning points and their approximate location - the type of each turning point (local or absolute, max. or min.) (If you can not nd some item, then state why not) Make a graph of the function and clearly label all the features. 2.a) A function has exactly 3 zeroes; they are -1, 0, and 2. The function passes through the point (1,6). Sketch the function. Find the equation of the function. h) A 4th degree function has minima at (-3,-5) and (3,-6) and a y-intercept at (0,3). Sketch the function. Find the equation of the function. (HINT: If the minima were on the x-axis then this would be easy. How can you move them? WARNING: a question like this may be on the test and/or summative. Make sure you know how to do it.) 3. Find the asymptotes of the following rational function, q(x). Find its asymptotes. If it does not have a particular type of asymptote (x) _ 5x - 1 (vertical, horizontal, or oblique) then briey say why it does not. x 2 ._ 2x _ 3 Describe the end behaviour of the function. Find its intercepts. Make a graph of the function. Draw and label the asymptotes and other features. 4. Abel needs x minutes to package a case of 24 widgets. Brian can fill a case in 3 minutes less time than Abel. Working together, they can ll a case in 12.32 minutes. How much time does Abel need when he is working alone? [Hintz How many widgets can Abel, Brian, or the team package in one minute?]