Math Quiz - Function Transformations & Quadratic Functions PDF

- [2.5: Function transformations] - - Know all the different types of function transformations and how they are represented graphically and algebraically. You need to understand transformations if they are given in terms of generic function notation (li...

- [2.5: Function transformations] - - Know all the different types of function transformations and how they are represented graphically and algebraically. You need to understand transformations if they are given in terms of generic function notation (like g(x)=2f(x-5)+8) OR if they are given in terms of a specific parent function (like g(x)=2(x-5)\^3+8). - Given a point on the parent function y=f(x), find the corresponding point on a given transformation g of f. - Given the graph of function y=f(x), sketch the graphs of various transformations of f. - [2.6: Combining functions] - - Know how to combine functions using algebraic operations (addition, subtraction, multiplication, and division) and using function composition. - You must be able to evaluate combined functions algebraically, numerically, and graphically. - [2.7: Inverse functions] - - Know what an inverse function is and how it is defined. - Know how to use function composition to verify if two given functions are inverses of one another. - Know how to algebraically find a formula for an inverse function. - If given a graph of a function y=f(x), sketch the graph of the inverse function of f. (That is, make sure you understand the graphical relationship between inverse functions.) - [3.1: Quadratic functions] - - Be able to identify a quadratic function expressed in any form. - Know the basic terminology related to quadratic functions (vertex and axis of symmetry). - Use the \"completing the square\" technique to express a quadratic function in vertex form and then from the vertex form identify the vertex and the axis of symmetry. - Know when a parabola opens up or down. Know when the vertex is a relative maximum point or a relative minimum point. - Know how to find the x-intercepts of a quadratic function expressed in vertex form. - Find the range of a quadratic function.