MAT129 Fall 2024 Notes

M September 30	Topics:	3.4,3.7	Notes:	09.25a, 09.25b, 09.25c, 09.25d, 09.30a, 09.30b, 09.30c, 09.30d
3.4 -Composition of Functions, pg. 209,  Learning Objectives
	* Combine functions using algebraic operations.
	* Create a new function by composition of functions.
	* Evaluate composite functions.
	* Find the domain of a composite function.
	* Decompose a composite function into its component functions.
3.5 -Transformation of Functions, pg. 222,  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
3.7 -  Inverse Functions, pg. 254,  Learning Objectives
	* Verify inverse functions.
	* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.
	* Find or evaluate the inverse of a function.
	* Use the graph of a one-to-one function to graph its inverse function on the same axes.

• Dilation of a Function by another Function - Polynomial & Rational Functions
• parabola.gsp --
• compositeFX.gsp  -- build 2 functions using other functions
• compositeFx.poly.ratl.gsp   -- build functions using other functions
  0 - graph of 1 function
  1 - graphs of 2 functions
  2 - composite of 4 functions
  3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
  4 - rational, rational function features & how to find them
  5 - end behavior, battle of (Ax^m)/(Bx^n)
• COMPOSITION -- Composition of Functions
• Dilation notes
• Dilation creates functions
• dilation by a constant animation
• composite functions  -- build 2 functions using other functions
compositeFX.gsp --
• compositeFx.poly.ratl.gsp
  0 - graph of 1 function
  1 - graphs of 2 functions
  2 - composite of 4 functions
  3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
  4 - rational, rational function features & how to find them
  5 - end behavior, battle of (Ax^m)/(Bx^n)

• inverse functions, definition & examples
• Inverse Notes: inverse functions: verbally, analytically, algebraically
• Inverse Problems
• Take An Inverse In 4 Language Families

• inverse.gsp
  0 - vertical, horizontal line tests
  1 - square root fx
  2 - any function
  3 - sqrt fx by parameters
  4 - restricted domain on inverse
  5 - arcsine
  6 - arctangent
  7 - f and inverse
  8 - f, inverse, tangents --

© 9/3/2024, A2 http://www.mathnstuff.com/math/precalc/129/M.09.30.htm