Need this done by Friday as I cannot be bothered doing it as I have an essay, an op-editorial and a poster due.
Australian Catholic University Melbourne Campus MATH107 Foundations of Mathematics Assignment, Part 3 Due: 3.00 p.m. Friday, May 18th, 2018. You should show all working for all your answers. (Marks will be awarded for working/explanations/correct notation as well as for correct answers.) Assignment parts are to be placed in the School of Arts Assignment Box located outside the School of Arts reception, Room 412.G.09A, 34-36 Brunswick St. Fitzroy (enter via Graham St.). Make sure that you have written your name and your student number on the front page. Make sure you attach an assignment cover sheet to your assignment. Late assignments will not be accepted. 9. In this question, let α be the last digit of your student number, β be the second last digit of your student number and γ be the third last digit of your student number. So, if your student number is S00123456 then α = 6, β = 5 and γ = 4. Use the shortest path algorithm to find the shortest path between A and B in the following graph: A B 2 γ + 4 8 β + 2 α + 1 6 5 7 4 6 1 3 3 9 5 1 7 9 1 [5 marks] Three more questions follow below ... Semester 1, 2017 Australian Catholic University Melbourne Campus 10. Consider the function f whose formula is given by f(x) = 1 log(x2 − x− 6) . (a) Find functions g and h so that f(x) can be written in the form g ◦ h(x). (b) State the (largest) domain and range of f . (Make sure you give detailed reasons for your answer.) [6 marks] 11. Consider the following equation:( a3 + b2 1 + 2t )−1 = (1 + c2t)( √ d− e), for real variables a, b, c, d, e and t. Express t as a function of a, b, c, d, e. (Make sure you show all your working.) [3 marks] 12. In this question, let α be the last digit of your student number, β be the second last digit of your student number and γ be the third last digit of your student number. So, if your student number is S00123456 then α = 6, β = 5 and γ = 4. (a) Find the slope of the function f(x) = (α + 1)x3 − x2 + (β + 1)x + 31 at the point x = −1. (Make sure you show all your working.) (b) The graph of the function f(x) = x4 4 + 2x3 3 − x 2 2 − 2x+ 1 is displayed below. Use the graph to write down the set of all points for which f has negative slope: Semester 1, 2017 Australian Catholic University Melbourne Campus -4 -3 -2 -1 0 1 2 3 4 5 -2 -1 1 2 3 4 [6 marks] Semester 1, 2017