Functions, Polynomials, and Graphs: Math Assignment (Weeks 2-4)

This assignment solution covers various topics in algebra, including functions and their graphs, transformations, polynomial and rational functions. The solution begins with determining the domain and range of functions using graphs, expressing them in both set-builder and interval notations. It then proceeds to evaluate functions at specific points and analyze increasing, decreasing intervals, and relative maxima/minima. The assignment delves into identifying even, odd, and neither functions and solving linear equations, including finding the slope, y-intercept, and equation in slope-intercept form. Furthermore, it addresses function transformations, finding the domain of various functions, and performing algebraic operations on functions such as addition, subtraction, multiplication, division, and composition. The solution also includes finding the inverse of a function. The assignment further explores parabola graphs by identifying maximum/minimum values, vertex, and axis of symmetry. It covers finding zeros, multiplicities, and writing polynomial equations from graphs. Additionally, the solution involves modeling real-world scenarios using quadratic functions and analyzing the end behavior, intercepts, and symmetry of polynomial functions.