Overview
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra II KHauck |
| Book: | Overview |
| Printed by: | Guest user |
| Date: | Sunday, 19 May 2024, 2:51 PM |
Description
Overview
Part 1
The purpose of this unit is to become familiar with rational functions. Specifically, in this unit you will learn:
- To add, subtract, multiply, divide, and simplify rational expressions
- To solve rational equations
- To analyze the graphs of rational functions
Rational functions are seen in many areas of study such as science, engineering, business, and economics. They are as varied as the volume of a cardboard box, the fuel efficiency of a car, and the cost per meal served at a restaurant. An understanding of rational functions is therefore important not only for further study of mathematics, but for understanding the world in which we live.
Part 2
Rational functions are functions of the form 
, where n(x) and d(x) are polynomial expressions and 
. Thus, 
and 
are rational functions, while 
and 
are not rational functions, since 
and sin x are not polynomials.
Expectations
MI Alg2 High School Content Expectations
Addressed Within the Rational Functions Unit.
L1.2.1 Use mathematical symbols to represent quantitative relationships and situations.
A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.
A1.1.4 Add, subtract, multiply, and simplify polynomials and rational expressions.
A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.
A1.2.5 Solve polynomial equations and equations involving rational expressions and justify steps in the solution.
A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.
A1.2.9 Know common formulas and apply appropriately in contextual situations.
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.
A2.1.6 Identify the zeros of a function, the intervals where the values of a functions are positive or negative, and describe the behavior of a functions as x approaches positive or negative infinity, given the symbolic and graphical representations.
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).
A2.2.2 Apply given transformations to parent functions, and represent symbolically.
A2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representations; recognize that different families of functions have different asymptotic behavior.
A2.3.3 Write the general symbolic forms that characterize each family of functions.
A2.4.1 Identify the family of functions best suited for modeling a given real-world situation.
A2.4.2 Adapt the general symbolic form of a function to one that fits the
specifications of a given situation by using the information to replace arbitrary constants with numbers.
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
A3.6.1 Write the symbolic form and sketch the graph of simple rational functions.
A3.6.2 Analyze graphs of simple rational functions and understand the relationship between the zeros of the numerator and denominator, and the function’s intercepts, asymptotes, and domain.