What are some key concepts covered in the Rational Expressions and Functions unit of the connexus math curriculum?
In the Rational Expressions and Functions unit of the Connexus Math curriculum, you will cover several key concepts. Here are some of the main topics:
1. Rational expressions: You will learn what rational expressions are and how to simplify, add, subtract, multiply, and divide them. This includes factoring and canceling common factors.
To study this concept, you can refer to your textbook or online resources that explain the rules and examples of simplifying and performing operations with rational expressions.
2. Solving rational equations: You will learn how to solve equations that involve rational expressions. This includes finding the domain and any restrictions in the solution set.
To solve rational equations, you can use the process of clearing fractions by multiplying both sides of the equation by the least common denominator (LCD) of all the denominators involved.
3. Graphing rational functions: You will explore the graphs of rational functions and understand their key features. This includes identifying horizontal and vertical asymptotes, holes, and x-intercepts.
To graph rational functions, you need to find the intercepts, asymptotes, and plot a few additional points. You can also use a graphing calculator or online graphing tool to visualize the graph.
4. Operations with rational functions: You will learn how to perform additions, subtractions, multiplications, and divisions with rational functions.
To perform operations with rational functions, you need to find the LCD, simplify the expressions, and then apply the respective operation based on the problem.
5. Applications of rational functions: You will explore real-life applications where rational functions can be used to model and solve problems. Examples could include rates, distances, or time.
To solve real-life application problems involving rational functions, it is important to understand the problem context and translate it into mathematical expressions. Then, solve the resulting equations or inequalities.
Throughout this unit, it is beneficial to practice solving problems, simplify expressions, and analyze graphs. Online resources, video tutorials, or practice websites can provide additional examples and exercises to reinforce your understanding of these concepts.