Radical Functions, Rational Exponents, and Inverse Functions: Math Unit 4, Grade 11 (Letters & Devotion)

Description

Radical Functions, Rational Exponents, and Inverse Functions is Unit 4 of Algebra II: Functions, Structure, and Modeling (Grade 11), the Letters & Devotion Math course, complete in one printable PDF: 10 lessons, the unit check-up and the answer key, 71 pages.

• The definition of a rational exponent as an extension of integer exponent rules
• Simplification of radical/rational-exponent expressions and denominator rationalization
• Radical equations and the extraneous-solution check
• The non-reversibility of squaring as the mechanism producing extraneous solutions
• The horizontal line test and the formal definition of a one-to-one function
• The structural distinction between one-to-one and many-to-one functions as it determines invertibility
• The algebraic procedure for finding and verifying an inverse function by composition
• Domain restriction as the method for creating an invertible piece of a non-one-to-one function
• Invertibility determined from algebraic structure alone, generalized beyond graphed function families
• Discriminant interpretation and rational-equation extraneous solutions, as long-retention targets

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.