Introduction to Quantitative Analysis (MAT136)

Scenario: In RadicRealm, players embark on an adventurous quest to solve radical equations and unlock magical abilities. Traversing diverse landscapes, they face challenges, solve puzzles, and interact with wise sages. By successfully unraveling radical equations, players gain new powers and confront the RadicSorcerer, restoring balance to the realm. RadicRealm sharpens critical thinking and problem-solving skills, transforming players into skilled RadicExplorers.   Task:  Solve: √x−7=x-7

Scenario: A powerful Artificial Intelligence has taken control of a virtual realm, distorting the rational functions that govern its existence. Players, as skilled mathematicians, enter the virtual realm and engage in epic battles against the AI's minions. To defeat them, players must find the horizontal and vertical asymptotes of the rational functions and strategically exploit their knowledge to overcome the challenges.   Task:  Find the intercepts and the vertical and horizontal asymptotes that would be used to sketch a graph of the function.    f(x)=x+2x2−25

Scenario: In PolyPuzzle, players navigate through a mystical labyrinth, solving complex polynomial expressions using grouping and factoring. By unraveling the puzzles and defeating the Polynomial Guardian, players restore harmony to the realm, honing their algebraic skills and problem-solving abilities.   Task:  Solve the following polynomial equation by grouping and factoring.   9y3−16y=0

Scenario: In PolyQuest, players journey through captivating landscapes, analyzing polynomial functions to identify their degree and leading coefficient. Challenges and guidance from mystical beings aid their progress. By unraveling the mysteries, players restore harmony to the realm, honing their analytical skills and mathematical intuition.   Task:  Give the degree and leading coefficient of the following polynomial function.   f(x)=x7(7−6x4−4x4)

Scenario: The kingdom is facing a catastrophic event of limited resources and a growing population. As heroic mathematicians, players must rescue the kingdom. They will explore treacherous terrains, solve puzzles, and use the mathematical skills to find solutions that prevent disaster and restore stability.   Task:  A town’s population increases at a constant rate. In 2010 the population was  57,000 . By 2012 the population had increased to  80,000 . If this trend continues, predict the population in 2016.

Scenario: Players enter a mystical realm where numbers and equations are scattered throughout. They must navigate through an enchanted forest, solving absolute value equations to progress. The forest is filled with floating equations, each presenting a unique challenge. Players must simplify the equations, isolate the absolute value expressions, and find both positive and negative solutions. Along the way, they battle mathematical creatures and interact with wise mathematicians who provide guidance and additional equations. Rewards and clues help players advance. The ultimate goal is to reach the Tree of Equations, restore its power, and break the curse that has plagued the realm. Through Equation Enigma, players practice solving absolute value equations while developing critical thinking and problem-solving skills. Task:   Solve the equation.   |2x+7|−6=6