Determine the end behavior, maximum number of turning point(s), and maximum number ofintercepts of the following polynomial functions:(a) .(b) .(c) .(d)(e)(f)XAVIER SCHOOLSenior High School Standard ProgramGRADE 11 GENERAL MATHEMATICSSecond Semester, S.Y. 2023-2024x−P(x) = − x 3 + 20x 2 + x + 10P(x) = 15x 3 − 18x 2 + 4x − 8P(x) = 13x 4 − 2x 3 + 5x 2 + x − 6P(x) = (x + 1)(3 − x)(3x − 1)(4x + 1)P(x) = (2x − 1) 2 (1 − x)(5 − 3x)2P(x) = − (x − 1)(x + 3)2 (2 + 3x)3

Consider a polynomial function 𝑓 ( 𝑥 ) = − 1 300 ( 𝑥 − 2 ) 2 ( 𝑥 − 3 ) ( 𝑥 + 1 ) 2 ( 𝑥 + 4 ) ( 𝑥 − 5 ) f(x)= 300 −1 ​ (x−2) 2 (x−3)(x+1) 2 (x+4)(x−5). Choose the correct set of options. The function 𝑓 ( 𝑥 ) f(x) has exactly 7 turning points. The function 𝑓 ( 𝑥 ) f(x) has exactly 6 points where the slope is 0. The function 𝑓 ( 𝑥 ) f(x) is neither even nor odd function. In the interval 𝑥 ∈ ( 3 , 5 ) x∈(3,5), 𝑓 ( 𝑥 ) f(x) is increasing first and then decreasing. The function 𝑓 ( 𝑥 ) f(x) is negative when 𝑥 ∈ ( − 1 , 2 ) x∈(−1,2).

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.

mine if the graph can represent a polynomial function. If so, assume the end behavior and all turning points are represented o

The height of a roller coaster at a given time is modeled by the polynomial function ℎ(𝑡)=(−0.01𝑡3+0.35𝑡2−3.5𝑡+10)(𝑡+5)2(𝑡−5)(𝑡+1)(2−𝑡)3h(t)=(−0.01t 3 +0.35t 2 −3.5t+10)(t+5) 2 (t−5)(t+1)(2−t) 3 , where t represents time in seconds. Find the turning point(s) of the height function.6758

1. A polynomial function can have more than one y-intercepts. (True/False)2. An increasing polynomial function is always one-to-one. (True/False)3. A polynomial function of degree s can have s + 1 zeros. (True/False)4. There is a turning point between any two zeros of a polynomial function.(True/False)5. If a critical point (turning point) of a polynomial function p(x) exists,then p(x) is not one-to-one. (True/False)