Original PromptCreata a student facing handout for pre-calculus review lesson/test corrections to go over the most missed concepts on our recent functions test. Include a do now with 2 error analysis questions. The first do now problem should be a composition question of g(f(x)) where f(x)=3x-4 and g(x)=x^2+2 but the student distributes the exponent instead of using foil. The second do now problem should be an error analysis where they were supposed to find the AROC for f(x)=x^2-2x on [1,4] but students did 8-...
This document focuses on reviewing functions through error analysis and piecewise graphing. Students are tasked with analyzing and correcting errors in function compositions and average rate of change (AROC) calculations. It includes a mini-lesson on how to graph piecewise functions, detailing steps such as identifying boundaries, evaluating endpoints, and sketching each piece. Guided and independent practice activities involve graphing various functions and exploring parent functions, with an emphasis on understanding open and closed circles for boundaries. Additionally, students engage in self-reflection and metacognitive assessments to enhance their understanding of piecewise functions.