Functions and Transformations Chapter 2.7 By Caitlyn McCall

Vocabulary Family graph- a group of graphs that display one or more similar characteristics Parent graph- graph of a parent function Parent function- simplest graph in a family

Types of Functions Constant Linear or Identity Absolute Quadratic

Constant Function Straight horizontal line y = a Domain= all real numbers Range= the value of a

Linear or Identity Function Straight diagonal line y = x Domain= all real numbers Range= all real numbers

Absolute Value Function Diagonal lines shaped like a V f(x) = |x| Domain= a set of real numbers Range= a set of real numbers greater than or equal to 0

Quadratic Function Curved like a parabola f(x) = x² Domain= set of real numbers Range= set of real numbers greater than or equal to 0

Transformations of Functions Translations Reflections Dilations (Wania)

Translations y = x² ± a moves up or down y = (x ± a)² moves left or right

Reflections y = -x² reflects on the x axis y = (-x)² reflects of the y axis

Dilations y = ax² a>1, graph stretches vertically a<1, graph compresses vertically

Problem #1 Graph the function and describe the transformations 1. y = 2(x-2)² Answer: Vertically stretched Translated right 2 units

Problem #2 Graph the function and describe the transformations 2. y = -(x-3)² -5 Answer: Reflected on x axis Translated right 3 units Translated down 5 units

Problem #3 Select the correct equation for the function y = x² -1 y = x² + 1 y = (x -1)² y = (x +1)² y = x² -1 y = x² + 1 y = (x -1)² y = (x +1)²

Problem #4 Select the correct equation for the function y = -|x+3|+6 y = -|x+6|+3 y = -|x+3|-6 y = -|x-3|+6 y = -|x+3|+6 y = -|x+6|+3 y = -|x+3|-6 y = -|x-3|+6