Final answer:
The student learned how to solve rational equations by finding a common denominator, identify extraneous solutions, graph rational functions including asymptotes and intercepts, and apply these concepts to real-world problems.
Step-by-step explanation:
In Module Four, I focused on three lessons that enhanced my understanding of rational equations and concepts. The first skill I mastered was solving rational equations by finding a common denominator, which is essential for simplifying and solving any equation where variables appear in the denominator. The second concept was understanding and identifying extraneous solutions, which may arise after clearing denominators and are not valid solutions to the original equation.
My third skill involved graphing rational functions, learning how to identify asymptotes and intercepts, which are key features of their graphs. Lastly, I honed my ability to apply these skills in real-world scenarios, analyzing situations where ratios and proportional relationships are used, such as in work-rate and shared-work problems.
Throughout this module, in-chapter examples and end-of-chapter exercises consistently reinforced these skills, providing a reliable method for ensuring my understanding deepened.