# Basic/Parent Functions
* * their purposes
* * an introduction to functions as a direct consequence of operations, page 10, "Finally ... Functions." It shows how functions compute & work.
* see https://www.mathnstuff.com/math/spoken/here/2class/80/math.htm
* Library of Functions - graphs, descriptions, information about specific functions
* Precalc & Calc Function Summaries, Summary Worksheets, and Collected Images, graphs
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/300fxGraphs/FXallWIDE.jpg
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/300fxGraphs/300fxFULL.pdf
* Parent Functions, Their Slope Functions, and Area Functions
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/parents.htm
* * their descriptions, domains, ranges, inverses, derivatives, …
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/library.htm
* Who Has Games
* Lines Of All Kinds Who Has -- Uses instructions which include vertical, horizonal, perpendicular, parallel, slope, intercept.
* see https://www.mathnstuff.com/papers/games/whohas/lines.htm
# 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)
* Summary of some curve shifting, reflections, and other composition as in y = af(bx-c)+d
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/kid.fx.sp24/children.pdf
* 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
# Inverse Functions
* inverse.gsp - -- take an inverse of an invertable function, horizontal & vertical line tests, includes arcfunctions
* see /www.mathnstuff.com/math/gsp/sumr19/su19newgsp/inverse.gsp
* Important Functions & Their Inverses as a Graph & a Calculator Button
* see https://www.mathnstuff.com/math/spoken/here/2class/300/invfn1.gif
* Take the inverse of 4 different functions
* see https://www.mathnstuff.com/math/spoken/here/2class/300/invfp.htm
* Take an inverse function using words or order of operations, graphically, or symbolically
* see https://www.mathnstuff.com/math/spoken/here/2class/300/invfn2.gif
* Take an inverse algebraically & graphically
* see https://www.mathnstuff.com/math/spoken/here/2class/300/invfn4.gif
* Take an inverse in Each of the Math Class Language Families
* see https://www.mathnstuff.com/math/spoken/here/2class/300/inverse.htm
# More sophisticated functions -created by inverses & by multiplication and/or division of constants and functions
* The Creation of New Functions -- Composition
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/comp.htm
* Curve Shifting because of Addition & Subtraction
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/shift.htm
* Dilations Create Functions -- Multiplication, Dilation, by A Constant
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/dilat.htm
* Dilation Creates Polynomial & Rational Functions
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/detour.htm
* Notes on Polynomial Functions -- Multiplication, Roots
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/polyn.htm
* Graphing Polynomial Functions -- Multiplication, Roots
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/poly.htm
* Graphing Rational Functions -- Division
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/rationl.htm
* Who Has Games & Connect-the-Dots
* Polynomial Functions Who Has? -- Includes single roots, double roots, concavity, end behavior, reflection about y = 0.
* see https://www.mathnstuff.com/papers/games/whohas/polyfx.htm
* Rational Functions Who Has? -- Add a discontinuity, remove a root, change the horizontal asymptote.
* see https://www.mathnstuff.com/papers/games/whohas/rationl.htm
# EXPONENTIAL or POWER FUNCTIONS -- growth is not constant as in y=mx+b, but proportional as in y=ab^x
* Exponential vs Linear Growth
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/linvexp.htm
* A Bit about e, the base of the natural log
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/expofx.htm
* Even More About e, the base of the Natural Logs
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/expofx.htm#e
* Linear vs Exponential Growth
* see https://www.mathnstuff.com/math/spoken/here/2class/300/fx/library/e.htm
* Log Functions - inverses of exponentials
* Use of log-log plane and semi-log plane
* see https://www.mathnstuff.com/math/spoken/here/2class/340/loggraf.htm
* Examples of Logs to Illustrate Characteristics & Mantissas
* see https://www.mathnstuff.com/math/spoken/here/2class/340/example.htm
* Laws/Rules of Logrithmic Computation and An Opportunity to Experiment with Common Log Computation
* see https://www.mathnstuff.com/math/spoken/here/2class/340/loglaws.htm
* Use of log-log plane and semi-log plane
* see https://www.mathnstuff.com/math/spoken/here/2class/340/loggraf.htm
* log-log plane, no axes
* see https://www.mathnstuff.com/math/spoken/here/2class/340/gif/loglog.gif
* semi-log plane, no axes
* see https://www.mathnstuff.com/math/spoken/here/2class/340/gif/semilog.gif
* Height at adulthood based on birth length and percentiles on logistic curve
* see https://www.mathnstuff.com/papers/height.htm
* Who Has Games & Connect-the-Dots
* Who Has? Exponential
* see https://www.mathnstuff.com/papers/games/whohas/expontl.htm
* Logarithm Connect-the-Dots
* see https://www.mathnstuff.com/papers/condots/logdots.htm
* see https://www.mathnstuff.com/papers/condots/conpdf/LBELL.pdf
* Exponent Connect-the-Dots
* see https://www.mathnstuff.com/papers/condots/exp.htm
* see https://www.mathnstuff.com/papers/condots/conpdf/LPHONE.pdf
* Expand or simplify the log Connect-the-Dots
* see https://www.mathnstuff.com/papers/condots/logbig.htm
* see https://www.mathnstuff.com/papers/condots/conpdf/LGBREAD.pdf
# Trig functions - cyclic functions most basically based on the central angle of circles and the ration of the length of the side of triangles
* TAN GENTS AND OTHER THINGS OF INTEREST
* see https://www.mathnstuff.com/math/spoken/here/2class/330/c33pg00.htm
* Interactive Trig Sketch Pad Material
* see https://www.mathnstuff.com/math/spoken/here/2class/330/c33pg00.htm#announcement
* Spread Sheets -- Dynamic Computation
* see https://www.mathnstuff.com/math/spoken/here/2class/330/c33pg00.htm#xls
* Angle Measure
* see https://www.mathnstuff.com/math/spoken/here/2class/260/angle.measure.htm
* Radians & Sectors Using the radianSector.gsp: Sketchpad, worksheet, answers, video local video,
* see https://www.mathnstuff.com/video/video.htm#radiansector
* see https://www.youtube.com/watch?v=dxHrbgIgYz0
* Arc and arc functions
* see https://www.mathnstuff.com/math/spoken/here/2class/330/arc.htm
* Connect-the-Dots
* Connect-the-Dots
1. "Dig the Change from Degrees to Radians Connect-the-Dots" ex. 180° = __ rad.
* see https://www.mathnstuff.com/papers/condots/TSHOVEL.pdf
2. "Oscar Had A Heap of Apples Connect-the-Dots" ex. easy: sin (A) of right triangles
* see https://www.mathnstuff.com/papers/condots/TAPPLE.pdf
3. "Trig Functions of Special Angles (in Degrees) in All Quadrants Connect-the-Dots" -- sin(30°)
* see https://www.mathnstuff.com/papers/condots/TCABIN.pdf
4. "Writing First Quadrant Trig Expressions Connect-the-Dots" -- sin(350°)
* see https://www.mathnstuff.com/papers/condots/TSCISSORS.pdf
5. "Slow Is the Way to Go Connect-the-Dots" ex. Find legs & angles of 30-45-60 right triangles
* see https://www.mathnstuff.com/papers/condots/TTURTLE.pdf
6. "EASIER If It Fits, Wear It -- sin(A) w/terminal side through (-3,4)
* see https://www.mathnstuff.com/papers/condots/TSHOE.pdf
7. HARDER "Find Sides & Angles of a Right Triangle" - sides, hypotenuse, angles of a right triangle.
* see https://www.mathnstuff.com/papers/condots/TICECREAM.pdf
8. "Oscar Reutersvard's Penrose Triangle" -- You Can Draw It. You Can't Build It. -- csc(300°)
* see https://www.mathnstuff.com/papers/condots/TNONTRIANGLE.pdf
9. "Can't Hold A ___ To You" -- Easier sin(A) w/Terminal Side through Point (-3, 4)
* see https://www.mathnstuff.com/papers/condots/TCANDLE.pdf
10. "2 Hours of Trig" -- Simplify Trig and Arcfunction Expressions, Solve Equations,
* see https://www.mathnstuff.com/papers/condots/2hrA.pdf
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