3.2 Families of Graphs Objectives: Identify transformations of simple graphs. Sketch graphs of related functions.

An anchor graph from which other graphs in the family are derived. Parent Graph: An anchor graph from which other graphs in the family are derived. Pg. 137 Parent graphs Ex. 1) Graph f(x)=x³ and g(x)=-x³. Describe how the graphs of g(x) and f(x) are related.

Use the parent graph y = x³ to sketch the graph of each function. Ex. 2) Use the parent graph y = x³ to sketch the graph of each function. a.) y = x³ - 1 b.) y = (x – 1)³ c.) y = (x – 1)³ + 3 Ex. 3)  

Transformations Model -works for linear,quadratic,cubic,absolute value,square root, etc. f(x) = - a (-cx – h)² + k Reflect over x-axis Reflect over y-axis Shift left or right Shift up or down Vertical Stretch/shrink (expands/compresses) a>1 →stretch (expand) 0<a<1 →shrink (compress) Horizontal Stretch/shrink c>1 →shrink 0<c<1 →stretch

Ex. 4) Observe the graph of each function. Describe how the graphs in part b and c relate to the graph in part a. a.) f(x) = (x+1)² - 2 f(x) = (x+1)-2