MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.5.htm © 2025   A2, Agnes Azzolino Graphing functions; Shifting, Reflecting, Stretching and Shrinking graphs. Text 3.5, PG. 222

Welcome to Precalc! Children Functions Hi,     You "know" the basic precalc functions, the "parent functions." Now examine these shifted, stretched, shrunk, the "children functions."     Contact me through the pink box on www.mathnstuff.com/math/math.htm or with the phone number on your class CANVAS home page.     Stay safe, A2

3.5 - Transformation of Functions Learning Objectives
	* Graph functions using vertical and horizontal shifts.
	* Graph functions using reflections about the x-axis and the y-axis.
	* Determine whether a function is even, odd, or neither from its graph.
	* Graph functions using comp

• Curve Shifting because of Addition & Subtraction of Functions
• Stretching & Shriking because of dilation by a constant
• parentFX gsp   -- function "manipulatives"
• parentFX2 gsp   -- revised function "manipulatives"
• 2 graphed functions
• Children of the parents created by translation/shifting, reflection/multiplication by a negative
  * Curve Shifting because of Addition & Subtraction
        * see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/shift.htm (shift)
  * The Creation of New Functions -- Composition
        * see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/comp.htm (compose)
  * Who Has Games & Connect-the-Dots
        * Function Curve Shifting Who Has? (Translations, Rotations, Reflections, Dilations)
              * see https://www.mathnstuff.com/papers/games/whohas/shift.htm
• Who Has? Curve Shift
• Math Exercises -- whole body graphing