Do Now: Graph the point and its image in a coordinate plane. 1. P -5, 3; reflected in the y -axis 2. Q -4, -3; reflected in the x -axis

1.1/1.2 Transformations of Linear Functions Objective: To understand Function Families and how transformations effect them.

Transformations Function Family: group of functions with similar characteristics Parent Function: most basic function in a family Transformation: changes the size, shape, position, or orientation of a graph. Translations Reflections Stretches Shrinks

Parent Functions you should recognize

Translations Transformation that shifts a graph horizontally or vertically. The size, shape, or orientation are NOT changed.

Horizontal and Vertical Translations

Example 1 Let 𝑓 𝑥 =2𝑥−1 Graph 𝑔(𝑥)=𝑓(𝑥)+3 Graph h(𝑥)=𝑓 (𝑥+3) Describe the transformations

Reflections Transformation that flips a graph over a line called the line of reflection.

Example 2 Let 𝑓 𝑥 = 1 2 𝑥+1 Graph 𝑔 𝑥 =−𝑓(𝑥) Graph ℎ 𝑥 =𝑓(−𝑥) Describe the transformations

Stretches and Shrinks Vertical Shrink ( 0 < a < 1) Shrinks towards the x-axis Vertical Stretch (a > 1) Stretches away from the x-axis

Stretch and Shrink

Example 3 Let 𝑓 𝑥 =𝑥−1 Graph 𝑔 𝑥 = 1 3 𝑓 𝑥 Graph ℎ 𝑥 =3𝑓 𝑥 Describe the transformations.

Homework Textbook Pages 16-17 3, 6, 9, 11, 16, 17, 18 Class contract Summer assignment