In this unit, students will:
- Explore Rational and Radical Functions.
- Determine rational numbers extend the arithmetic of integers by allowing division by all numbers except zero. Similarly, rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial.
- Notice the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.
- Investigate the properties of simple rational and radical functions and then expand their knowledge of the graphical behavior and characteristics of more complex rational functions.
- Recall and make use of their knowledge of polynomial functions as well as compositions of functions to investigate the characteristics of these more complex rational functions.
- Solve equations and inequalities involving rational and radical functions.
- Understand that not all solutions generated algebraically are actually solutions to the equations and extraneous solutions will be explored.
- Apply these rational and radical functions with an emphasis on interpretation of real world phenomena as it relates to certain characteristics of the rational expressions.