MAT129 Fall 2025 Notes
mathnstuff.com/math/precalc/MAT129fa25/p.4.htm
© 2025   A2, Agnes Azzolino
Review of lines, slopes and functions
. Text 3.1-3.3, 4.1, PG. 160, 174, 160, 180, 187, 196, 280

Welcome to Precalc!
Say A Rule In Words, In Symbols, In Pictures, Even With "Toys"
 
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Instant Reference Material:
Graphs of "all" functions     Summary of "all" functions 
Library of Functions     Symbols & words in gif format
Function Note Cards animation     web page     flash cards 
3.1 - Functions and Function Notation, pg. 160,  Learning Objectives
	* Determine whether a relation represents a function.
	* Find the value of a function.
	* Determine whether a function is one-to-one.
	* Use the vertical line test to identify functions.
	* Graph the functions listed in the library of functions.
3.2 -  Domain and Range, pg. 180,  Learning Objectives
	* Find the domain of a function defined by an equation.
	* Graph piecewise-defined functions.
3.3 - Rates of Change and Behavior of Graphs, pg. 196,  Learning Objectives
	* Find the average rate of change of a function.
	* Use a graph to determine where a function is increasing, decreasing, or constant.
	* Use a graph to locate local maxima and local minima.
	* Use a graph to locate the absolute maximum and absolute minimum.
4.1 - Review of slopes and functions, pg. 280,  Learning Objectives
	* Represent a linear function.
	* Determine whether a linear function is increasing, decreasing, or constant.
	* Interpret slope as a rate of change.
	* Write and interpret an equation for a linear function.
	* Graph linear functions.
	* Determine whether lines are parallel or perpendicular.
	* Write the equation of a line parallel or perpendicular to a given line.
    ************ fx.library ************

Functions: Graphs, Vocabulary, Details
domain range real zeros
Graphs jpg Details pdf Library web pages
ODD/EVEN definitions       odd/even/neither smile
odd definition even definition Symbols & words gif


Basic Functions
identity function opposite reciprocal function
squaring function square root function
absolute value function and absolute value
piecewise defined greatest integer function


Function Sketchpads
line.gsp   -- slide points A and B and generate equation of the line in 4 forms.
reciprocal gsp, 1/x, etc.   -- reciprocal functions
    * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
absolute value gsp  -- |x|, functions controlled by parameters and NOT controlled by parameters
2graphs.gsp  -- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
graphs gsp  -- 1 or 2 graphed functions ready to edit
squaring gsp, parabola   -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms, ...
square root gsp   -- 2 square root functions defined by easy-edit parameters
piece-wise gsp   -- graphs a piecewise defined function when left function and right function
absValu.gsp  -- 2 absolute value functions controlled by parameters
greatest integer function gsp, [[x]] -- also a[[bx+c]] + k
reciprocal functions   -- graph of parameter-defined reciprocal function,
    * with slide-able tangent line,
    * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
composite functions gsp  -- build 2 functions using other functions
inverse gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
parentFX gsp   -- function "manipulatives"
parentFX2 gsp>   -- revised function "manipulatives"
Instant Reference Material:
Graphs of "all" functions     Summary of "all" functions 
Library of Functions     Symbols & words in gif format
Function Note Cards animation     web page     flash cards
Rise Over Run with Coordinates & Slope of the Tangent
 
 
First point:
(, )  
Second point:
(, ) 
 
Press:
for the slope.