LESSON Reteach 1-7 Function Notation

1 Copyright by Holt, Rinehart and Winston. 54 Holt Algebra 2 All rights can use Function Notation to write a Function . f(x) 2x 3 Evaluate f (0), f 1 __ 2 , and f ( 2) for f (x) 2x 2 x 1. f (0) 2(0) 2 0 1 1f 1 __ 2 2 1 __ 2 2 1 __ 2 1 2 1 __ 4 1 __ 2 1 1 __ 2 1 __ 2 1 1f ( 2) 2 ( 2) 2 ( 2) 1 2(4) 2 1 8 2 1 11 For each Function , evaluate f (0), f 3 __ 2 , and f ( 1). (x) 4 x 2 2f (0) 4 (0) 2 2 f 3 __ 2 4 3 __ 2 2 2 f ( 1) 4( 1) 2 2 272 (x) 2x 10f (0) 10 f 3 __ 2 7 f ( 1) 12 (x) x 2 6xf (0) 0 f 3 __ 2 45 ___ 4 f ( 1) 5 Name Date ClassReteachFunction Notation1-7 LESSONRead: f of x equals 2x f (x)Input xSubsitute 0 for x in the Function and 1 __ 2 for 2 for Sec1 Sec1:5412/20/05 1:47:18 PM12/20/05 1:47:18 PMProcess BlackProcess BlackCopyright by Holt, Rinehart and Winston.

2 55 Holt Algebra 2 All rights Date ClassPlot ordered pairs on a coordinate plane to graph a Function . Y XTo graph f x 2x 3, make atable of 2x 3f x 2 2 2 37 1 2 1 350 2 0 331 2 1 312 2 2 3 1 Graph each Function on the coordinate plane given. 4. x 2x 4x2x 4g x 02 0 4 412 1 4 222 2 4032 3 4242 4 44 ReteachFunction Notation (continued)1-7 LESSONV alues between given points are not defined. Do not connect the points. Y X All points are defined. Connect the points.

3 Y X Sec1 Sec1:555/5/06 12:44:38 PM5/5/06 12:44:38 PMProcess BlackProcess BlackCopyright by Holt, Rinehart and Winston. 87 Holt Algebra 2 all rights reserved .#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/. * >V Vi &UNCTION .OTATION&IND EACH VALUE OF THE Function F S X D X F S D S D Y X Y X Y X F S D F S D F S D F S D F S D F S D F S D F S D F S D 'RAPH EACH Function F S X D X Y X Y X 4Y USES THE Function G S X D S X D TO CALCULATE THE COST IN DOLLARS OF USING A CALLING CARD TO MAKE A LONG DISTANCE CALL LASTING X MINUTES 4HE VARIABLE X MUST BE A WHOLE NUMBER 'RAPH THE Function 4 HEN DETERMINE THE COST OF A MINUTE CALL ,ENGTH OF #ALL MIN #OST OF #ALL #ALLING #ARD #OSTS XY#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !))))

4 LGEBRA !LL rights reserved ,%33/. * >V Vi &UNCTION .OTATION&OR EACH Function EVALUATE F T E F T E F T ?? E G S X D X H S X D X ?? F S X D X X ?? F S X D X ?? ?? ?? 'RAPH EACH Function 4 HEN EVALUATE F T E AND F T E F S X D X F S X D ?? X Y X Y X 3 OLVE /N ONE DAY THE VALUE OF 5 3 WAS EQUIVALENT TO EURO /N THE SAME DAY 5 3 WAS EQUIVALENT TO #ANADIAN 7 RITE A Function TO REPRESENT THE VALUE OF #ANADIAN DOLLARS IN EUROS 7 HAT IS THE VALUE OF THE Function FOR AN INPUT OF ROUNDED TO THE NEAREST CENT AND WHAT DOES IT REPRESENT F T C E C ????? F T E THE VALUE OF #ANADIAN IS EQUIVALENT TO EUROS 0# (AVEN SELLS COMPUTERS AT A DISCOUNT ON THE ORIGINAL PRICE PLUS A REBATE 7 RITE A Function TO REPRESENT THE FINAL PRICE OF A COMPUTER AT 0# (AVEN 7 HAT IS THE VALUE OF THE Function FOR AN INPUT OF AND WHAT DOES IT REPRESENT F T P E P F T E IS THE FINAL DISCOUNTED PRICE OF A COMPUTER WITH AN ORIGINAL PRICE OF #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !))))

5 LGEBRA !LL rights reserved ,%33/.* >V Vi &UNCTION .OTATION ! SET OF INPUT VALUES IS SOMETIMES REFERRED TO AS THE REPLACEMENT SET FOR THE INDEPENDENT VARIABLE %VALUATE EACH Function FOR THE GIVEN REPLACEMENT SET F S X D X ??? O ?? P G S X D X S X D O ?? ?? P ?? ?? ??? Y X Y X O ?? P O ?? P ?? ?? ?? ?? ?? %XPLAIN WHAT A REASONABLE DOMAIN AND RANGE WOULD BE FOR EACH SITUATION THE NUMBER OF SLICE PIZZAS NEEDED TO FEED X PEOPLE AT A PARTY WHERE EACH PERSON WILL EAT SLICES OF PIZZA THE TIME IT TAKES TO BICYCLE M MILES AT A RATE OF MILES PER HOUR 7 RITE A Function TO REPRESENT EACH SITUATION 3 HARON EARNS FOR EACH LAWN SHE MOWS F T A E A %ACH LARGE TUB OF ICE CREAM MAKES SINGLE DIP CONES ! SINGLE DIP CONE SELLS FOR F T T E T T E 0 OSSIBLE ANSWER 4HE DOMAIN IS A POSITIVE WHOLE NUMBER X REPRESENTING THE NUMBER OF PEOPLE AT A PARTY THE RANGE IS A POSITIVE WHOLE NUMBER X ?

6 ?? REPRESENTING THE NUMBER OF PIZZAS NEEDED 0 OSSIBLE ANSWER 4HE DOMAIN IS A POSITIVE RATIONAL NUMBER M REPRESENTING THE NUMBER OF MILES TRAVELED THE RANGE IS A POSITIVE RATIONAL NUMBER M ??? REPRESENTING THE TIME REQUIRED #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved 9OU CAN USE Function Notation TO WRITE A Function F X X %VALUATE F F S ?? D AND F FOR F X X X F F S ?? D S ?? D ?? S ?? D ?? ?? ?? F &OR EACH Function EVALUATE F F T ?? E AND F F X X F F S ?? D S ?? D F F X X F F S ?? D F F X X XF F S ?? D ??? F ,i i>V &UNCTION .OTATION ,%33/.2 EAD F OF X EQUALS X /UTPUT F X )NPUT X3 UBSITUTE FOR X IN THE Function AND EVALUATE 3 UBSTITUTE ?? FOR X 3 UBSTITUTE FOR X 875/5/06 12:50:59 PM5/5/06 12:50:59 PMCopyright by Holt, Rinehart and Winston.)

7 88 Holt Algebra 2 all rights reserved .#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved 0 LOT ORDERED PAIRS ON A COORDINATE PLANE TO GRAPH A Function Y X4O GRAPH F S X D X MAKE A TABLE OF VALUES X X F S X D S D S D S D S D S D 'RAPH EACH Function ON THE COORDINATE PLANE GIVEN G S X D X X X G S X D T E T E T E T E T E ,i i>V &UNCTION .OTATION CONTINUED ,%33/.6 ALUES BETWEEN GIVEN POINTS ARE NOT DEFINED $O NOT CONNECT THE POINTS Y X !LL POINTS ARE DEFINED #ONNECT THE POINTS Y X #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/. > i }i&UNCTION 4 OGETHERNESS 9OU CAN THINK OF A Function AS A PROCESS 4HE PROCESS HAS AN INPUT THE INDEPENDENT VARIABLE 4 HAT INDEPENDENT VARIABLE IS PUT INTO THE Function PROCESSED AND THEN OUTPUT AS THE DEPENDENT VARIABLE 3O F S X D X DEFINES THE PROCESS PERFORMED BY THE Function F 4HE VARIABLE X IS INPUT MULTIPLIED BY AND THEN IS ADDED TO THE RESULT 4HE OUTPUT IS THE RESULT OF THE PROCESS #ONSIDER THE FUNCTIONS F S X D X AND G S X D X X $ESCRIBE THE PROCESS OF THE FUNCTIONS F AND G IN WORDS F TAKES A NUMBER DOUBLES IT AND SUBTRACTS G SQUARES A NUMBER ADDS THE SAME NUMBER AND SUBTRACTS %VALUATE F S X D X %VALUATE G S X D X X !))))

8 COMBINATION OF THE FUNCTIONS F S X D AND G S X D FORM A COMPOSITE Function F S G S X D D )N F S G S X D D THE OUTPUT OF G S X D IS USED AS THE INPUT FOR F S X D 7 HICH Function OR PROCESS IS PERFORMED FIRST IN THE COMPOSITE Function F S G S X D D G %VALUATE THE COMPOSITE Function F S G S X D D AND SIMPLIFY YOUR RESULT X X %VALUATE THE COMPOSITE Function G S F S X D D AND SIMPLIFY YOUR RESULT X X )S IT TRUE THAT F S G S X D D G S F S X D D .O! COMMON Function USED IN MATH IS THE DIFFERENCE QUOTIENT F S X H D F S X D ????????????? H %VALUATE THE DIFFERENCE QUOTIENT FOR THE Function F AND SIMPLIFY YOUR RESULT %VALUATE THE DIFFERENCE QUOTIENT FOR THE Function G AND SIMPLIFY YOUR RESULT X H #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/.

9 * L i - }&UNCTION .OTATION *UAN IS ANALYZING CELL PHONE PLANS 4HE GRAPH SHOWS TWO PLANS HE IS CONSIDERING 5SE THE GRAPH FOR %XERCISES n &OR WHICH VALUE OF X DOES EACH Function HAVE A VALUE OF 0 LAN ! MIN PLAN " MIN 4HE GRAPHS OF THE FUNCTIONS CROSS AT X %XPLAIN WHAT THIS REPRESENTS 5SE Function Notation AND ESTIMATION TO REPRESENT THE VALUE OF EACH Function FOR MINUTES 0 LAN ! PLAN " *UAN EXPECTS TO USE ABOUT MINUTES PER MONTH 7 HICH PLAN SHOULD HE BUY 7HY 0 LAN " COSTS LESS THAN PLAN ! FOR MINUTES)N 3 EPTEMBER (ARLEY PUTS THAT HE EARNED DURING THE SUMMER IN A BANK ACCOUNT TO USE DURING THE SCHOOL YEAR FOR HIS PERSONAL EXPENSES (E BUDGETS D DOLLARS A MONTH FOR EXPENSES #HOOSE THE LETTER FOR THE BEST ANSWER 7 HICH SHOWS A Function REPRESENTING THE AMOUNT LEFT IN HIS ACCOUNT AFTER MONTHS !)

10 F S D D D" F S D D D# F S D D S D D$ F S D D ?????? D (ARLEY WRITES THE Function G S A D ?????? A TO SHOW HIS MONTHLY BUDGETED AMOUNT REMAINING IN A MONTH WHEN A THE ACTUAL AMOUNT HE SPENDS IS LESS THAN THE AMOUNT OF HIS BUDGET 7 HAT IS THE VALUE OF THIS Function FOR A MONTH WHEN HE SPENDS & ( ' * 4 IME MIN 0 LAN "0 LAN !#OST #ELL 0 HONE 0 LANS XY &AY USES THE Function F S X D ?? X TO FIND THE NUMBER OF BOXES OF TILE TO BUY FOR EACH SQUARE FEET OF FLOOR (OW MANY BOXES OF TILES DOES SHE NEED TO COVER SQUARE FEET ! BOXES" BOXES# BOXES$ BOXES 2 ASHEED USES THE Function F S E D E TO FIND THE DISTANCE AROUND A SQUARE BARBECUE PIT 7 HAT IS THE LENGTH OF THE SIDE OF THE PIT THAT HAS A PERIMETER OF FT & FT' FT( FT* FT 0 OSSIBLE ANSWER &OR MIN THE TWO PLANS COST THE SAME AMOUNT #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !))))))