identifying polynomial and rational functions, the domain, using the graphical representation of these functions, in this, we will examine and answer the behavior- discontinuities, increasing, decreasing and extrema.

please useGeoGebra graphing tool in graphing, https://www.geogebra.org/calculator

Task 1. Interpret the following graph in detail: (graph inserted below)

(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- 8x³-8x²+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 Task 3. Given a function

(i) Find the horizontal and vertical asymptotes.

(ii) Find the domain of rational function. Show all steps.

Task 4.

The following graph represents a rational function. (graph below)

(i)Identify the horizontalandvertical asymptotes (if any).Explain how you would find horizontalandvertical asymptotes of any rational function mathematically.

(ii)Identify thezeros of the rational function.

(iii) Identify the rational function.

Task 5.Before working on this task 5, please base it on the following reading:

Read page238of the following textbook will help you in understanding the concepts better.

Stitz, C., & Zeager, J. (2013).College algebra.Stitz Zeager Open Source Mathematics.https://stitz-zeager.com/szca07042013.pdf

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