Original PromptCreate a student facing pre-calculus practice test that covers the topics below. Each section should have 4-6 problems. The whole practice test should be 4 pages in length:
Function Basics & Composition
•Domain & Range: Determining the domain for polynomial, rational, and square root functions using interval and set-builder notation.
•Composition of Functions: Algebraically evaluating and simplifying composite functions, such as `
f(g(x))
f(g(x))`.
•Composite Domains: Finding the restricted dom...
This resource focuses on Advanced Functions with an emphasis on Composition & Rational Analysis. It includes practice on analyzing, manipulating, and graphing functions such as rational, piecewise, and composite functions. Students will learn to evaluate composite functions and determine their restricted domains using interval notation, identify points of discontinuity, and demonstrate function transformations and rate of change mastery. The document also covers algebraic symmetry proofs, average rates of change, graphical analysis, piecewise function mastery, and transformation applications. Students will engage in various tasks assessing their understanding of these concepts through algebraic manipulations, graphical constructions, and error analysis, ultimately leading to a comprehensive understanding of advanced function behavior and characteristics.