Ch.+1+Function+Transformation

Chapter 1: Transformations

Ch. 1 Function Transformation

**Learning outcome **

 * ===Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations. ===
 * ===Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: • x-axis • y-axis • line y = x ===
 * ===Demonstrate an understanding of the effects of horizontal and vertical stretches (expansions/ compression) on the graphs of functions and their related equations ===
 * ===Apply translations and stretches (expansions/compression) to the graphs and equations of functions.Demonstrate an understanding of inverses of relations. ===
 * ===Apply translations and stretches (expansions/compression) to the graphs and equations of functions.Demonstrate an understanding of inverses of relations. ===

__Class Notes __

 * ==**// [[file:K 1.1 - Basic Functions - Horizontal & Vertical Translations key.pdf|Section 1.1– Basic Functions Horizontal & Vertical Translations]] //**==
 * **//[[file:K 1.2 - Vertical & Horizontal Reflections.pdf|Section 1.2 - Vertical & Horizontal Reflections]]//**
 * **//[[file:K 1.3 – Expansions and Compressions key.pdf|Section 1.3 – Expansions and Compressions]]//**
 * //**[[file:K 1.4 A – Combining Transformations key.pdf|Section 1.4 – Combining Transformations .]]**//
 * //**[[file:K 1.5 – Inverse of a Relation key.pdf|Section 1.5 – Inverse of a Relation]]**//
 * ===//Quiz 2 1.1-1.5//===


 * == [[file:Transformations_Govt_Exam_Question.pdf|Extra transformations Gov.Exam]] ==
 * == [[file:Transformations_Govt_Exam_Questions_Answer_Key.pdf|Extra transformations Gov. Exam key]] ==

forms y-k=f(x) and y=f(x-h), respectively A translated graph is congruent to the original graph.
=== **__Reflection__** – A transformation where each point of the original graph has an image point resulting from a reflection in a line. May result in a charge of orientation of a graph while preserving its shape. ===

__**Stretch**__ – A transformation in which the distance of each x-coordinate or y-coordinate from the line of reflection is multiplied
**by some scale factor.**

Scale factors between 0 and 1 result in the point moving closer to the line of reflection; scale factors greater than 1 result in the point moving farther away from the line of reflection.
=== **__Inverse of a function -__** is a function with domain A and range B, the inverse function, if it exists, is denoted by f-1 and has domain B and range A. f-1 maps y to x if and only if f maps x to y. ===