MAT129 Fall 2025 Notes
mathnstuff.com/math/precalc/MAT129fa25/p.7.htm
© 2025   A2, Agnes Azzolino
Functions, composition of functions. Text 3.4, 3.5, 3.7, PG. 222, 209, 254

Welcome to Precalc!
A Function of a Function
Hi,
    We have been composing functions for most of the semester.
    For example the function y = 3(x - 2)2 + 6 is really
    x - take a number
    x-2 - subtract two from that result
    (x - 2)2 - square that result
    3(x - 2)2 - multiply by 3
    3(x - 2)2 + 6 - add six to that result
   
    If needed, 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

See Last Class

 
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.
3.7 Inverse Functions