MAT129 Fall 2024 Notes

M September 16	Topics:	3.1, 3.2, 3.3, 4.1	Notes:	09.16a graphs of parent functions I, 09.16b graphs of parent functions, II, 09.16c, 09.16d
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.

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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

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"

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.

• rate
• slope
• secant
• tangent
• difference quotient
• Take a Derivative Using the Limit of the Difference Quotient image
• asymptote
• ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
  0 - toc, history
  1 - only 1 function
  2 - parabola w/tangent line
  3 - cubic w/tangent line
  4 - polynomial
  5 - rational
  6 - compute slope drag 2 points
  7 - dy/dx by definition
  8 - m= given A, B
  9 - 3 points define a parabola
  10 - notes on 3 points define a parabola
• DerAnyFx -- Derivative of Any Function
      * One may trace the function and see coordinates displayed.
      * One may edit the function.
      * One may graph the approximate derivative function.
        1 - f(x) w/tangent line
        2 - f(x) & TRACE
        3 - any f(x): x, f(x), f'(x), f''(x)
        4 - sin(x): x, f(x), f'(x), f''(x)
• 2graphs.gsp  -- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files

© 9/17/2024, A2 http://www.mathnstuff.com/math/precalc/129/M.09.16.htm