In this assignment, you will acquire the skills and knowledge to create the graph of function.We will be utilizing graphs to comprehend the various functions in this course. Graphs can be transformed into reversible mathematical functions, making them a valuable tool in visualizing and analyzing mathematical concepts. It is crucial to master graphing skills to effectively complete future assignments. Geogebra, an online graphing calculator, will be used throughout this course.Task 1. In this course, you will be instructed to use Geogebra to produce graphs. Discuss different features available in Geogebra related to graphs in this discussion forum such as point tools and axis settings. What are the steps to create a graph using Geogebra? Which features do you find interesting? Have you encountered any challenges while using it? You can also provide other comments related to creating graphs in Geogebra.Your Discussion should be a minimum of 150 words and maximum 250 in length. Please include a word count. Following the APA standard, use references and in-text citations for the textbook and any other sources.

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 - 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 behaviorTask 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.(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.Task 5. Before working on this task 5, please read the following reading:Read page 238 of 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.pdfAn 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?Submission Settings: Please complete all the 5 tasks in this assignment.You may use a word document that addresses the questions mentioned above. The word document should be double-spaced in Times New Roman font, which is no greater than 12 points in size.        Use APA citations and references if you use ideas from the readings or other sources. For assistance with APA formatting, view the Learning Resource Center: Academic Writing.       The document should be double-spaced in Times New Roman font, which is no greater than 12 points in size.       Use high-quality, credible, relevant sources to develop ideas that are appropriate for the discipline and genre of writing.        This assignment will be assessed by your instructor using the rubric below.

You are required to complete all the 4 tasks in this assignment. You can use scientific calculators or online scientific calculators for this assignment. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool. Show all steps wherever necessary. Task 1:After completing one revolution, point A is observed to have coordinates (() on the unit circle. Using that information, please answer the following questions:(i) Calculate all 6 values of the trigonometric functions (clearly state the formulae used to calculate these functions).(ii) Determine the quadrant in which the point lies and provide the reason.(iii) Calculate the angle formed by point A and the reference angle with the positive X-axis.Task2: Alice had been standing on the ground (Point A) and observing a brightly colored object resembling a bird on the top of a tree at a distance of 40 meters from the tree. She decided to get a closer look by moving 20 meters closer to the tree (Point B). After moving closer, she realized that the object was not a bird but something that she could catch. Then, she decided to catch it by climbing the tree, which had a height of 60 meters from the ground. Using the above scenario, please answer the following questions showing step by step calculations and stating the formulae.(i) Find the angles formed by Alice at the points A and B relative to the top of the tree. What are these angles called as?(ii) Determine whether angle A is larger than angle B. Make a conclusion about the comparison of angles when observing an object from a distance versus close.(iii) Find the distances between the object and points A and B.

The graph of a function g is shown.The x y-coordinate plane is given. A function labeled y = g(x) with 4 parts is graphed.The first part is a curve, enters the window in the second quadrant, goes up and right becoming less steep, crosses the y-axis at approximately y = 2.5, and ends at the open point (2, 3).The second part is a curve begins again at the open point (2, 1), goes up and right becoming less steep, and ends at the open point (5, 2).The third part is the closed approximate point (5, 1.2).The fourth part is a curve, begins at the open point (5, 2) goes down and right becoming more steep, and exits the window in the first quadrant.Use it to state the values (if they exist) of the following:(a)  lim x → 2− g(x)(b)  lim x → 2+ g(x)(c)  lim x → 2 g(x)(d)  lim x → 5− g(x)(e)  lim x → 5+ g(x)(f)  lim x → 5 g(x)SolutionLooking at the graph we see that the values of g(x) approach as x approaches 2 from the left, but they approach as x approaches 2 from the right.Therefore (a) lim x → 2− g(x) =     and    (b) lim x → 2+ g(x) = .Since the left and right limits are different, we conclude that (c) the limit as x approaches 2 of g(x) does not exist.The graph also shows that (d) lim x → 5− g(x) =     and    (e) lim x → 5+ g(x) = .This time, the left and right limits are the same and so, by this theorem, we have (f) lim x → 5 g(x) = Despite this fact, notice that g(5) ≠ 2.

The graph of a function g is shown. The x y-coordinate plane is given. The curve begins at the point (−2, 0), goes up and right, passes through the point (−1.5, 1), goes up and right, changes direction at the point (−1, 1.5), goes down and right, passes through the point (−0.5, 1), goes down and right, passes through the origin, goes down and right, passes through the point (0.5, −1), goes down and right, changes direction at the point (1, −1.5), goes up and right, passes through the point (1.5, −0.5), goes up and right, changes direction at the point (2, 0.5), goes down and right, crosses the x-axis at x = 2.5, goes down and right, changes direction at the point (3, −1), goes up and right, passes through the point (3.5, −0.5), goes up and right, and ends at the point (4, 0.5). Estimate 4 −2 g(x) dx with six subintervals using the following. (a) right endpoints 0 Correct: Your answer is correct. (b) left endpoints -0.5 Correct: Your answer is correct. (c) midpoints

The function g(x) is shown on the graph.What is the equation of g(x) in vertex form? g(x) = (x − 4)2 − 3 g(x) = (x − 4)2 + 3 g(x) = (x + 4)2 − 3 g(x) = (x + 4)2 + 3