## "Functions from a Standard 4.5 Perspective Grades 9 - 12"© Agnes Azzolino10/2014, AMTNJ

 Create and use mathematical processes and representations to organize and communicate mathematical ideas through concrete, pictorial, symbolic and graphic representations. Graph and take inverses in four modalities.

 Standard 4.5 REPRESENTATIONS Create and use representations to organize, record, and communicate mathematical ideas through concrete, pictorial, symbolic and graphic representations  Select, apply, and translate among mathematical representations to solve problems  Use representations to model and interpret physical, social, and mathematical phenomena

 The Languages of the Math Classroom© '98, '08, '09 Agnes Azzolino MOTHER TONGUE & OTHER TONGUE(S) Most Sophisticated and also the Most Basic MOSTLY MATH TONGUES Most Sophisticated, Most Basic VERBAL / Auditory WRITTEN / Symbolic PICTORIAL / Visual CONCRETE / Kinesthetic formal spoken mathematics written word DIGITAL MANIPULATIVE object informal spoken mathematics written symbol moving picture model spoken symbol semisymbolic static picture manipulative/token symbol speak calculator symbol numeral calculatoreze/computereze graph web speak nonverbal body language

 Graph   Graph by placement on the coordinate plane. DTWYP. a. the identity function b. the opposite function c. the reciprocal function d. e. f. g. h. i. y = (x - 4)˛ j. y = - (x - 2)˛ + 3 k. x = y˛m. n. the distance between a number and 3

 Solve Solve the statements by graphing 2 functions on the same plane: [a.] |x - 3| = 4 [b.] |x - 3| = 0 [c.] |x - 3| = -4 [d.] |x - 3| = |x + 2| [e.] |x - 3| = ( x + 2 )˛ + 1

 Take Inverses in Four Modalities         An example Some problems Resources The coordinate plane is at:         www.mathnstuff.com/gif/mciplane.gif . The inverse function problems are at:         www.mathnstuff.com/math/spoken/here/2class/300/invfp.htm Hand out for the Exploring Functions Lecture is at:         www.mathnstuff.com/papers/ef/efho.htm Math "Exercises"(www.mathnstuff.com/papers/langu/exerc.htm) a) Use your body, arms, and hands to represent the graph of: 1. y = 0 2. x = 0 3. y = x 4. y = -x 5. y = x˛ 6. x = y˛ 7. y = -2x˛ 8. y = - |x| 9. y = 2|x| 10. y = |x| - 2 11. y = |x| + 2 12. y = 1/x b) Please be seated.

 Thanks for Playing         © 10/2014, A2 www.mathnstuff.com/papers/amtnjeb.htm