# This assignment assesses your skills/knowledge on identifying polynomial and rat

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:(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.
Task 2. Given a polynomial: f(x) = x4 – 8×3 -8×2 +8x +7
(i)Use rational theorem and synthetic division to find the zeros of the polynomial
(ii) Draw the graph using GeoGebra graphing tool.
(iii) Identify its end behavior
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(i) Find the horizontal and vertical asymptotes.
(ii) Find the domain of rational function. Show all steps.
(i) Identify the horizontal and vertical asymptotes (if any). Explain how you would find horizontal and vertical asymptotes of any rational function mathematically.
(ii) Identify the zeros of the rational function.
(iii) Identify the rational function.
Stitz, C., & Zeager, J. (2013). College algebra. Stitz Zeager Open Source Mathematics. https://stitz-zeager.com/szca07042013.pdf
An online courier service is ready to transport a diverse range of items to ensure efficient delivery. The agency requires boxes of various dimensions. Let’s now focus on creating open boxes that have fixed height for storing these items. Take a cardboard of length thrice of the width and cut the edge of all 4 corners with 15cms, then fold the cardboard to get an open box.
Based on that information, answer the following questions:
(i) Find the volume of the open box, explain whether the resultant function is a polynomial or any other.
(ii) Find the possible domain for the volume function
(iii) If we wish to put a flexible item that has a volume of 12500 cubic cm, what dimensions of the box would be appropriate?
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