This assignment assesses your skills/knowledge on identifying polynomial and rational functions, the domain, using the graphical representation of these functions, and hence you will study the behavior- discontinuities, increasing, decreasing and extrema.

In real life situations the growth need not be smooth and always increasing or decreasing. The functional values may be having different turnings and may be disappearing at some points. These kinds of situations are represented by polynomial and rational functions. This assignment will enable you to identify such functions and interpret them mathematically and graphically.

You are required to complete all the 5 tasks in this assignment, answer the following questions, and show stepwise calculations. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool.



Task 1. Interpret the following graph in detail:

Image of Graph


(I) Identify the turning points, zeros, and x-intercepts.

(ii) Do you find any point or zero which has a multiplicity in the graph? If so, specify them with multiplicity and explain the reason.

(iii) Identify the degree and the polynomial as well as identify the domain in which the polynomial is increasing and decreasing.

(iv) Do we have local maximum/minimum here? If yes, find them.

(v) Find the remainder when the polynomial is divided by x-4.