Objective: I can understand transformations of functions. Families of Functions Objective: I can understand transformations of functions.

Vocabulary Parent Function Simplest form in a set of functions. Transformation: Change in the size or position of a function Translation: Moves a function horizontally or vertically Reflection: Reflects a function across a line of reflection Dilation: Changes a function size Domain: Set of all input values (x values) Range: Set of all output values (y values)

4 Parent Functions Absolute Value Quadratic 𝑦= 𝑥 Domain: all real numbers Domain: all real numbers Range: y 0 ≥ Range: 𝑦 ≥0

Square Root Cubic 𝑦= 𝑥 Domain: 𝑥 ≥0 Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 Range: 𝑦= 𝑥 Domain: 𝑥 ≥0 Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 Range: 𝑦 ≥0 Range: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

Dilations x y1 y2 -2 2 4 -1 1 Dilations: Vertical stretch compression Graph x y1 y2 -2 2 4 -1 1 Dilations: Vertical stretch compression

Translations Set your calculator window to: Graph x y1 y2 3 1 4 2 7 9 3 1 4 2 7 9 12 Vertical Translation: k units Up: Down:

Reflections x y1 y3 -2 error 1.4 -1 1 2 x y1 y2 1 -1 2 1.4 -1.4 3 1.7 Graph x y1 y3 -2 error 1.4 -1 1 2 x y1 y2 1 -1 2 1.4 -1.4 3 1.7 -1.7 Reflections: Across x-axis Across y-axis

Transformation of f(x) = 𝑥 Translation: Horizontal (k > 0) Translation: Vertical (k > 0) Right h units 𝑓 𝑥−ℎ Up k units 𝑓 𝑥 +𝑘 𝑓 𝑥+ℎ 𝑓 𝑥 −𝑘 Left h units Down k units 𝑥−ℎ 𝑥 +𝑘 Reflection Dilation: Vertical by a factor of a 𝑎⋅𝑓 𝑥 𝑎 𝑥 Across x-axis −𝑓 𝑥 − 𝑥 Stretch: 𝑎>1 𝑓 −𝑥 Across y-axis Compression: N/A 0<𝑎<1 𝑦=±𝑎 𝑥−ℎ +𝑘