#(!04%2 £Î -ÕÌÃÊiÞ 3EQUENCES AND &UNCTIONS !2% 9/5 2%!$9 0!'% LINEAR EQUATION SLOPE YINTERCEPT POINTSLOPE FORM 4HE PATTERN IS TO ADD TO THE NUMERATOR AND SUBTRACT FROM THE DENOMINATOR ??? ??????? ??? ??????? ??? ??????? 4HE NEXT THREE NUMBERS IN THE PATTERN ARE ??? ??? ??? 4HE PATTERN IS TO INCREASE EACH NUMBER BY THE NEXT LARGER ODD INTEGER 4HE NEXT THREE NUMBERS IN THE PATTERN ARE 4HE PATTERN IS TO ADD TO EACH INTEGER 4HE NEXT THREE NUMBERS IN THE PATTERN ARE 4HE PATTERN IS TO DECREASE EACH NUMBER BY ?? ? ? ? ? ?? ?? ?? ?? 4HE NEXT THREE NUMBERS IN THE PATTERN ARE ?? ?? A S B DC FOR A B C S D S D S D S D Y ??X SLOPE ?? YINTERCEPT 4HE LINE CROSSES THE YAXIS AT THE POINT S D AND MOVES UNITS UP FOR EVERY UNITS IT MOVES TO THE RIGHT Y X / Y ??X SLOPE ?? YINTERCEPT 4HE LINE CROSSES THE YAXIS AT THE POINT S D AND MOVES UNIT DOWN FOR EVERY UNITS IT MOVES TO THE RIGHT !24 &),% -4%?#?&%!? (27 Y #534/-%2 #2%!4%$ "9 %$)4%$ "9 FP / CREATED 4)-% .%43 ONLY ALTERED MOD BLACKLINE V COMPLEX GREYSCALE (27 Y #534/-%2 %$)4%$ A B C FOR A B C "9 FP COLOR / S AB D C FOR A B C S D S D S A B D C FOR A B C QÊ S D R S D S D S D S D CREATED $!4% 4)-% X 4%#( */" .5-"%2 $!4% "9 .%43 COMPLEX Y X SLOPE YINTERCEPT 4HE LINE CROSSES THE YAXIS AT THE POINT S D AND MOVES UNITS UP FOR EVERY UNIT IT MOVES TO THE RIGHT !24 &),% -4%?#?&%!? #2%!4%$ $!4% SIMPLE */" .5-"%2 $!4% X 4%#( .%43 SIMPLE BLACKLINE ONLY ALTERED MOD COMPLEX GREYSCALE .%43 V COMPLEX COLOR 4%#( !24 &),% -4%?#?&%!? (27 #534/-%2 #2%!4%$ "9 FP %$)4%$ "9 */" .5-"%2 $!4% $!4% 4)-% #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED -C$OUGAL -ATHEMATICS CREATED(OLT .%43 ONLY ALTERED SIMPLE MOD COMPLEX .%43 V COMPLEX ?? ALREADY IN SIMPLEST FORM Y X Y ??? ?????? X Y ??X SLOPE ?? YINTERCEPT 4HE LINE CROSSES THE YAXIS AT THE POINT S D AND MOVES UNITS UP FOR EVERY UNITS IT MOVES TO THE RIGHT ??? ?? ??? ?? 0!'%3 n Y 4HINK AND $ISCUSS 0OSSIBLE ANSWER &IND THE DIFFERENCES BETWEEN THE SUCCESSIVE TERMS TO SEE IF THERE IS A COMMON DIFFERENCE X / 0OSSIBLE ANSWER &IND THE FIRST TEN TERMS BY REPEATEDLY ADDING THE COMMON DIFFERENCE 4HE TENTH TERM IS S D !LSO BY USING THE FORMULA THE TENTH TERM IS S D S D Y X %XERCISES Y X Y ??? ???????? X -4%?#?&%!? 4%#( ??X !24 &),% Y (27 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON */" .5-"%2 #534/-%2 DIFFERENCE OF SLOPE ?? YINTERCEPT FP #2%!4%$ "9 $!4% 4HE LINE CROSSES THE YAXIS AT THE POINT S D AND %$)4%$ "9EVERY UNITS IT MOVES $!4% MOVES UNITS DOWN FOR TO 4)-% THE RIGHT 4HE SEQUENCE IS NOT ARITHMETIC Y CREATED .%43 ONLY ALTERED .%43 ?? ?? ?? ?? ?? COMPLEX SIMPLE MOD COMPLEX V GREYSCALE COLOR BLACKLINE ?? ?? ?? ?? X / 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON DIFFERENCE OF ?? X Y 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON Y X DIFFERENCE OF Y ???? ??????? X ???? x ? ?? ??? ??? ?4%#( -4%?#?&%!? Y ??X!24 &),% (27 #534/-%2 */" .5-"%2 ??? ???? SLOPE ?? YINTERCEPT ??? ?? FP #2%!4%$ "9 $!4% 4HE LINE CROSSES THE YAXIS AT THE POINT S D 4HE SEQUENCE IS NOT ARITHMETIC %$)4%$ "9 $!4% AND MOVES UNIT UP FOR EVERY UNITS IT MOVES TO 4)-% THE RIGHT Y CREATED .%43 SIMPLE MOD BLACKLINE ONLY ALTERED COMPLEX GREYSCALE .%43 V COMPLEX 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON COLORDIFFERENCE OF X / #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED !24 &),% -4%?#?&%!? (OLT -C$OUGAL -ATHEMATICS 4%#( ?? ?? ?? ? ? ? ? ? ? ?? ? ? ? ? N N Y N N Y N N N N N N ?? ?? x ?? ?? ?? 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON DIFFERENCE OF ?? 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON DIFFERENCE OF N N Y N N N &IND THE TH TERM A N A S N DD A S D A S D A A &IND THE TH TERM A N A S N DD A S D A S D A A A D A N A N A N D N N N N N 4HE PACKAGE WEIGHS OUNCES #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED ?? ?? ?? x ?? ?? ?? ?? 4HE SEQUENCE IS NOT ARITHMETIC N N Y N N Y N N N N N N Y N N &IND THE ST TERM A N A S N DD A S D S D A S D S D A S D A &IND THE TH TERM A D A N A S N DD A S D A S D A A ?? ?? Y N Y N ?? Y N ?? N ?? ?? ?? ?? ?? ?? Y ??N Y N N Y ?? ?? ?? N ??N &IND THE TH TERM AN A SN DD A S D S D A S D S D A S D A &IND THE RD TERM A N A S N DD A S D A S D A A (OLT -C$OUGAL -ATHEMATICS &IND THE TH TERM A D A N A S N DD A S D A S D A A A D A A A 4HE FIRST FOUR TERMS OF THE SEQUENCE ARE &IND THE TH TERM A D A N A S N DD A S D S D A S D S D A S D A A A A A A A B A N A S N DD A S D A S D A A C A N A S N DD S N D N N N N LAPS )DENTIFY THE ARITHMETIC SEQUENCE A D A N A N A S N DD S N D N N N N /SCAR RACED FOR HOURS A D A A A A 4HE FIRST FIVE TERMS ARE A D A A A A 4HE FIRST FIVE TERMS ARE A D A A A A 4HE FIRST FIVE TERMS ARE )DENTIFY THE ARITHMETIC SEQUENCE A D A N A N A S N DD S N D N N N N IS THE TH TERM A D A A A A A 4HE FIRST FOUR TERMS OF THE SEQUENCE ARE #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED 0OSSIBLE ANSWER 7HAT ARE THE FIRST TWO TERMS OF THE ARITHMETIC SEQUENCE WITH A AND D !NSWER AND 0OSSIBLE ANSWER 3UBTRACT EACH TERM FROM THE NEXT TERM TO FIND THE COMMON DIFFERENCE )F THE COMMON DIFFERENCE IS POSITIVE THE TERMS OF THE SEQUENCE ARE INCREASING )F IT IS NEGATIVE THEY ARE DECREASING 4HE CONSECUTIVE TERMS ARE A N AND A N A N S A N D A N A N A N SO A N 3OLVE FOR N A N S N D S N D N N N N N 4HE CONSECUTIVE TERMS ARE AND AND THEY ARE THE TH AND TH TERMS # )DENTIFY THE SEQUENCE A D A N A S N DD S N D N N N N A D A N A S N DD A S D A S D A A (OLT -C$OUGAL -ATHEMATICS Y ??? Y X ?? ?? ? X ? K K &IND THE TH TERM R ?? A N A R N A S D &IND THE ST TERM ?? ?? ?? ?? ?? ? ? R ??? ?? A N A R N ?? C ?? C "IASED POSSIBLE ANSWER 4HE QUESTION LEADS PEOPLE TO AGREE WITH hEXPERTSv .OT BIASED POSSIBLE ANSWER 4HE QUESTION DOES NOT LEAD PEOPLE TO GIVE A PARTICULAR RATING 0!'%3 n 4HINK AND $ISCUSS 0OSSIBLE ANSWER )N AN ARITHMETIC SEQUENCE A CERTAIN NUMBER THE COMMON DIFFERENCE IS ADDED TO EACH TERM TO FIND THE NEXT TERM )N A GEOMETRIC SEQUENCE A CERTAIN NUMBER THE COMMON RATIO IS MULTIPLIED BY EACH TERM TO GET THE NEXT TERM 0OSSIBLE ANSWER $IVIDE EACH TERM BY THE TERM BEFORE IT ?? UNDEFINED 4HE SEQUENCE IS NOT GEOMETRIC 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? ?? ?? ?? ?? x 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF (EATHERS STARTING SALARY IS A AND IF SHE GETS A RAISE EVERY TIME SHE IS ELIGIBLE SHE WILL RECEIVE RAISES 3INCE EACH RAISE IS AFTER EACH RAISE SHE WILL MAKE OR TIMES HER PREVIOUS SALARY SO THE COMMON RATIO IS A R N A N A R N A S D y )F (EATHER GETS A RAISE EVERY TIME SHE IS ELIGIBLE AFTER YEARS SHE WILL MAKE PER HOUR %XERCISES A ?? S D ?? ?? ?? ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? x ?? ??? ?? ??? ?? ?? 4HE SEQUENCE IS NOT GEOMETRIC ?? ?? ?? 4HE SEQUENCE IS NOT GEOMETRIC 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ??? ?? ?? x ??? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? ?? ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? ?? ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED (OLT -C$OUGAL -ATHEMATICS A R 4HE FIRST FIVE TERMS ARE &IND THE TH TERM ?? R ?? ?? A N A R N A ?? S D A R S D S D S D S D 4HE FIRST FIVE TERMS ARE &IND THE TH TERM R ????? ???? A N A R N ??? A ???? &IND THE TH TERM ?? ?? R ??? A N A R N A ?? ??? A R 4HE FIRST FIVE TERMS ARE S D A R ?? ?? ? ? ? ? ?? 4HE FIRST FIVE TERMS ARE S D &IND THE TH TERM R ?? A N A R N A S D ??? ?? ?? &IND THE ST TERM ??? ??? R ??? ??? A N A R N S D ?? A ??? A R 4HE FIRST FIVE TERMS ARE &IND THE TH TERM R ??? A N A R N A S D 4HE STARTING POINTS ARE 3INCE ONE FIFTH OF THE TOTAL POINTS ARE ADDED AT THE END OF EACH LEVEL AND ONEFIFTH IS THE NUMBER OF POINTS WILL BE TIMES HIGHER AT THE END OF EACH LEVEL A R N A N A R N A S D 4HERE ARE POINTS AT THE END OF THE FIFTH LEVEL A COMMON RATIO ?? ?? ? ? ?? 4HE NEXT THREE TERMS ARE A COMMON RATIO 4HE NEXT THREE TERMS ARE #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED A R S D S D S D S D 4HE FIRST FIVE TERMS ARE R A ??? A N A R N A S D ??? A S D ??? ?? A A R A N A R N A S D A S D ?? A A ?? (OLT -C$OUGAL -ATHEMATICS A A A ??? ?? R ?? A A N A R N A ?? ??? A A ??? A N A R N ?? A ??? A A A ?? R ??? A N A R N A ?? A ??? A 4HERE ARE TWO TEAMS LEFT IN THE SIXTH ROUND S D S D S D S D S D S D 4OWN ! A R N A N A R N A S D A y 4OWN " A R N A N A R N A S D A y #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED 0OSSIBLE ANSWER 4HE STUDENT DIVIDED BY THE COMMON RATIO INSTEAD OF MULTIPLYING BY IT 4HE CORRECT ANSWER IS 0OSSIBLE ANSWER %VEN THOUGH BOTH SEQUENCES HAVE AS THEIR SECOND TERMS THE SEQUENCE WITH THE GREATER COMMON RATIO GROWS MUCH FASTER THAN THE SEQUENCE WITH THE LESSER COMMON RATIO A A 4HERE ARE DAYS IN THREE WEEKS 4HE CELLS TRIPLE EVERY DAYS SO YOU WANT TO KNOW HOW MANY CELLS THERE ARE AFTER THE CELLS HAVE TRIPLED TIMES 4HEREFORE N A R N A N A R N A S D A S D A 4HERE ARE CELLS AFTER WEEKS 3INCE YOU WANT TO KNOW HOW MUCH THE CAR IS WORTH AFTER YEARS N A R N A N A R N A S D A y 4HE CAR WILL BE WORTH APPROXIMATELY A #HECK TO SEE IF THERE IS A COMMON RATIO FOR THE VALUES IN THE HEIGHT ROW ?? ???? ?? ???? ?? ???? ?? ????? 4HE SEQUENCE COULD BE A GEOMETRIC SEQUENCE WITH A COMMON RATIO OF ?? B A R ?? N A N A R N A ?? A ?????? A y 4HE BALL WILL BOUNCE APPROXIMATELY FEET AFTER THE TH BOUNCE S D )F THE RATE CONTINUES 4OWN " WILL HAVE A GREATER POPULATION 4OWN ! WILL HAVE AN ESTIMATED POPULATION OF AND 4OWN " WILL HAVE AN ESTIMATED POPULATION OF A N A R N A A R A A R A ???? A R ?? R ?? A A R R R A ??????? SO R ?? A 'UESS AND CHECK TO FIND R SO R &IND A A N A R N A S D A S D A ???? &IND A A N A R N S D A ???? A # A R N A N A R N A S D A #HECK FOR A COMMON RATIO ?? ??? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? M ??? M S D S D ??? M X ??? X ??? X (OLT -C$OUGAL -ATHEMATICS X ??? X S D S D ??? IS FOLLOWED BY ONE MORE THAN ITS OPPOSITE 4HE NEXT THREE TERMS ARE S P D P P P P ! POSSIBLE RULE IS THAT THE SEQUENCE REPEATS THE PATTERN 4HE NEXT THREE TERMS ARE X X S X D X X X S Y D Y Y ! POSSIBLE RULE FOR THE SEQUENCE IS THAT IT IS THE LIST OF NEGATIVE PERFECT SQUARES S D S D AND SO ON 4HE NEXT THREE TERMS ARE 0!'%3 n 4HINK AND $ISCUSS N A N ????? N A ????? A ????? A ????? A ????? A ????? FIRST DIFFERENCES SECOND DIFFERENCES %XERCISES 3EQUENCE ST $IFFERENCE ND $IFFERENCE 4HE FIRST FIVE TERMS ARE ?? ?? ?? ??? A N S N D S N D A S D S D S D S D A S D S D S D S D A S D S D S D S D A S D S D S D S D A S D S D S D S D 4HE FIRST FIVE TERMS ARE 4HE NEXT THREE TERMS ARE 3EQUENCE ST $IFFERENCE ND $IFFERENCE N ????? A N N ????? A ????? A ????? A ????? A ????? A 4HE NEXT THREE TERMS ARE 3EQUENCE ST $IFFERENCE ND $IFFERENCE 4HE NEXT THREE TERMS ARE ST $IFFERENCE ND $IFFERENCE 4HE PRODUCT AC IS EITHER ONE MORE OR ONE LESS THAN B 4HE NEXT THREE TERMS ARE ??? x ?? ?? ?? ?? ?? 3EQUENCE ! POSSIBLE RULE IS TO ADD TO THE NUMERATOR AND DENOMINATOR OF THE PREVIOUS TERM 4HE NEXT THREE ??? ??? TERMS ARE ??? ST $IFFERENCE ! POSSIBLE RULE IS THAT EACH POSITIVE TERM IS FOLLOWED BY ONE LESS THAN ITS OPPOSITE %ACH NEGATIVE TERM #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED ?? ?? ? ? ?? ? ? ? ? 4HE FIRST FIVE TERMS ARE ?? ?? ?? 3EQUENCE ?? ?? ?? ? ? ?? ??? ND $IFFERENCE 4HE NEXT THREE TERMS ARE (OLT -C$OUGAL -ATHEMATICS 3EQUENCE ST $IFFERENCE ND $IFFERENCE 4HE NEXT THREE TERMS ARE 3EQUENCE ST $IFFERENCE ND $IFFERENCE 4HE NEXT THREE TERMS ARE A N N S N D N A S D S D S D A S D S D S D A S D S D S D A S D S D S D A S D S D S D 4HE FIRST FIVE TERMS ARE N A N ????? N S D A ????? S D A ????? S D A ????? S D A ????? S D A ????? ?? 4HE FIRST FIVE TERMS ARE ?? ?? ??? 3EQUENCE ST $IFFERENCE ND $IFFERENCE 4HE EVEN NUMBERS IN THE &IBONACCI SEQUENCE ARE AND 4HESE ARE THE RD TH TH TH TERMS 4HE NEXT FOUR EVEN NUMBERS WILL OCCUR IN THE TH TH ST AND TH TERMS ! POSSIBLE RULE FOR THE SEQUENCE IS A PATTERN OF A NUMBER AND ITS OPPOSITE THEN THE NEXT TERM IS ONE MORE THAN THE ORIGINAL NUMBER ALONG WITH ITS OPPOSITE AND SO ON 4HE NEXT THREE TERMS ARE ! POSSIBLE RULE FOR THE SEQUENCE IS TO FIRST ADD THREE TO THE PREVIOUS TERM TO FIND THE NEXT AND THEN SUBTRACT ONE FROM THE PREVIOUS TERM AND CONTINUE THIS PATTERN 4HE NEXT THREE TERMS ARE 4HE MULTIPLES OF ARE AND 4HESE ARE THE TH TH TH TERMS 4HE NEXT FOUR MULTIPLES OF WILL OCCUR IN THE TH TH TH AND TH TERMS 3EQUENCE ST $IFFERENCE ! POSSIBLE PATTERN IS THAT A ZERO IS ADDED BETWEEN THE DECIMAL POINT AND THE IN THE DECIMAL PART OF THE NUMBER 4HE NEXT THREE TERMS ARE ND $IFFERENCE 4HE NEXT THREE TERMS ARE ??? ???? ???? ?? ??? ! POSSIBLE RULE FOR THE SEQUENCE IS TO TAKE THE RECIPROCAL OF THE CUBE OF A NUMBER THAT INCREASES BY ONE EACH TERM 4HE NEXT THREE TERMS ARE ???? ???? ???? ?? ?? ?? ?? ?? ?? C IS EITHER ONE MORE OR ONE LESS THAN AE AND BD 4HE NEXT THREE TERMS ARE ????? A N N N ????? A ????? A ????? A ????? A ????? A ?? ? ? ?? ??? ??? ?? 4HE SEQUENCE OF THE FREQUENCIES ! ! ! ! IS ???? IT IS A GEOMETRIC ??? ???? "ECAUSE SEQUENCE 3O A AND R S D A N A R N S N D A N 4HE SEQUENCE OF HARMONICS IS "ECAUSE IT IS AN ARITHMETIC SEQUENCE WITH A COMMON DIFFERENCE OF A A 4HE FREQUENCY OF % IS (Z 4HE FIRST FIVE TERMS ARE ?? ?? ?? ?? #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED (OLT -C$OUGAL -ATHEMATICS 4HE SEQUENCE OF HARMONICS IS "ECAUSE IT IS AN ARITHMETIC SEQUENCE 3O A AND D A N A S N DD A N S N D A N N A N N 2%!$9 4/ '/ /. 0!'% 4HE SEQUENCE IS NOT ARITHMETIC 4HE SEQUENCE COULD BE ARITHMETIC WITH A COMMON DIFFERENCE OF 4HE SEQUENCE IS ????? ????? "ECAUSE ???? ????? ????? IT IS A GEOMETRIC ????? SEQUENCE 3O A AND R A N A R N S D A N N 4HE NOTE & IS THE TH NOTE IN THE SEQUENCE SO FIND A S D A A A y 4HE NOTE & WOULD HAVE A FREQUENCY OF ABOUT (Z 4HE SEQUENCE IS NOT ARITHMETIC &IND THE TH TERM A D A N A S N DD A S D A S D A &IND THE TH TERM A D A N A S N DD A S D S D A S D S D A &IND THE TH TERM ?? ?? A D ?? A N A S N DD A S D?? A S D?? A ?? ????? # A N N N ??? ?????? A ????? A N N N ?? ????? A ?? ??? ??? 4HE SEQUENCE IS NOT GEOMETRIC &IND THE TH TERM A D A N A S N DD A S D A S D A ?? ??? ??? ??? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? ??? ???? ???? 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF A D A N A N A S N DD S N D N N N N #ARMEN WILL MAKE BRACELETS IN THE ST WEEK 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF ?? 4HE SEQUENCE IS NOT GEOMETRIC #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED (OLT -C$OUGAL -ATHEMATICS 3EQUENCE 4HE SEQUENCE COULD BE GEOMETRIC WITH A COMMON RATIO OF &IND THE TH TERM A R ??? A N A R N A A A ST $IFFERENCE ND $IFFERENCE ND $IFFERENCE A N N A S D A S D A S D A S D A S D 4HE FIRST FIVE TERMS ARE 0OSSIBLE ANSWER 4HE RULE FOR THIS SEQUENCE COULD BE THE TH POWERS 4HE NEXT THREE TERMS ARE 4HE NEXT THREE TERMS ARE #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED ?? ?? ?? ??? 0OSSIBLE ANSWER !DD TO THE PREVIOUS NUMERATOR AND DENOMINATOR ??? ??? 4HE NEXT THREE TERMS ARE ??? ST $IFFERENCE 4HE NEXT THREE TERMS ARE 3INCE THE MACHINE DEPRECIATES BY EACH YEAR ITS VALUE IS OR TIMES THE PREVIOUS YEARS VALUE 3O R 4HE END OF THE SIXTH YEAR IS THE BEGINNING OF THE SEVENTH YEAR SO N A S D 4HE VALUE OF THE MACHINE AFTER YEARS IS ABOUT 3EQUENCE S D S D TH TERM A R ?????? ??? A N A R N A ??? A ??? A 4HE NEXT THREE TERMS ARE S D S D ND $IFFERENCE &IND THE TH TERM ?? A R ??? N A N A R A ?? A ?? y A ???? &IND THE TH TERM ?? ? ? ???? A R N A N A R A ?? S D A ?? S D A 3EQUENCE ST $IFFERENCE A N N A A A A A 4HE FIRST FIVE TERMS ARE A N S D N N A S D S D A S D S D A S D S D A S D S D A S D S D 4HE FIRST FIVE TERMS ARE A N S N D A S D A S D A S D A S D A S D 4HE FIRST FIVE TERMS ARE (OLT -C$OUGAL -ATHEMATICS 0!'%3 n 7RITE THE FUNCTION IN SLOPEINTERCEPT FORM F S X D X F S X D X 4HE FUNCTION IS LINEAR BECAUSE IT CAN BE WRITTEN IN THE FORM F S X D MX B 4HE SLOPE M IS n AND THE YINTERCEPT B IS 4HINK AND $ISCUSS 0OSSIBLE ANSWER 3UBSTITUTE THE YINTERCEPT AND THE COORDINATES OF A POINT ON THE GRAPH INTO THE EQUATION Y MX B AND SOLVE FOR M 7RITE THE EQUATION USING THE VALUES FOR M AND B THAT YOU FOUND 7RITE THE FUNCTION IN SLOPEINTERCEPT FORM F S X D X X F S X D X 4HE FUNCTION IS LINEAR BECAUSE IT CAN BE WRITTEN IN THE FORM F S X D MX B 4HE SLOPE M IS AND THE YINTERCEPT B IS ? 4HE FUNCTION F S X D ? X CANNOT BE WRITTEN IN SLOPE INTERCEPT FORM SO IT IS NOT LINEAR %XERCISES 7RITE THE FUNCTION IN SLOPEINTERCEPT FORM F S X D X X F SX D X 4HE FUNCTION IS LINEAR BECAUSE IT CAN BE WRITTEN IN THE FORM F S X D MX B 4HE SLOPE M IS AND THE YINTERCEPT B IS 4HE FUNCTION F S X D X CANNOT BE WRITTEN IN SLOPEINTERCEPT FORM SO IT IS NOT LINEAR 7RITE THE FUNCTION IN SLOPEINTERCEPT FORM F S X D X F S X D X 4HE FUNCTION IS LINEAR BECAUSE IT CAN BE WRITTEN IN THE FORM F S X D MX B 4HE SLOPE M IS AND THE YINTERCEPT B IS )DENTIFY THE YINTERCEPT FROM THE GRAPH B ,OCATE ANOTHER POINT S D 3UBSTITUTE INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M M M 4HE RULE IS F S X D X ,OCATE TWO POINTS &IND THE SLOPE M Y Y ????? M ??????? X X 3UBSTITUTE M AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR B F S X D MX B S D B B 4HE RULE IS F S X D X 4HE YINTERCEPT IS THE AMOUNT ,IZA MAKES WITH NO OVERTIME B )F ,IZA WORKS HOUR OF OVERTIME SHE EARNS SO ONE POINT ON THE LINE IS 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M M 4HE RULE IS F S X D X 7HEN ,IZA WORKS HOURS OF OVERTIME X F S X D X F F 7HEN ,IZA WORKS HOURS OF OVERTIME SHE EARNS #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED )DENTIFY THE YINTERCEPT FROM THE GRAPH B ,OCATE ANOTHER POINT 3UBSTITUTE INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M M ?? M 4HE RULE IS F S X D ??X ,OCATE TWO POINTS S D S D &IND THE SLOPE M Y Y ???????? M ??????? X X 3UBSTITUTE M AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR B F S X D MX B B B 4HE RULE IS F S X D X 4HE YINTERCEPT IS THE TOTAL AMOUNT OF WATER IN THE POOL B )F THE PUMP DRAINS FOR MINUTE THE AMOUNT OF WATER IN THE POOL IS SO ONE POINT ON THE LINE IS 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M M 4HE RULE IS F S X D X WHERE X THE AMOUNT OF TIME IN MINUTES 7HEN X F S X D X F S D F S D !FTER MINUTES THERE WILL BE GALLONS LEFT IN THE POOL (OLT -C$OUGAL -ATHEMATICS 4HE YINTERCEPT IS THE WEIGHT OF THE BABY AT BIRTH B !FTER MONTH THE BABY WEIGHS POUNDS SO ONE POINT ON THE LINE IS S D 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M S D M 4HE RULE IS F S X D X 7HEN X F S X D X F S D F S D 4HE BABY WEIGHS APPROXIMATELY POUNDS DURING THE SEVENTH MONTH B 0OSSIBLE ANSWER 7HAT IS F S D F S X D X F S D S D F S X D 0OSSIBLE ANSWER )F THE FUNCTION CAN BE WRITTEN IN THE FORM F S X D MX B THEN IT IS LINEAR 4HE ONLY KIND OF LINE ON A COORDINATE PLANE THAT IS NOT A LINEAR FUNCTION IS A VERTICAL LINE IT IS NOT A FUNCTION BECAUSE THE XVALUE HAS AN INFINITE NUMBER OF YVALUES /NE POSSIBLE VERTICAL LINE IS X A 4HE YINTERCEPT IS THE STARTING VALUE OF THE CAR B !FTER YEAR THE CARS VALUE IS SO ONE POINT ON THE LINE IS S D 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M S D M 4HE RULE IS F S X D X B 7HEN X F S X D X F S D S D F S D !FTER YEARS THE CARS VALUE WILL BE A 4HE YINTERCEPT IS THE STARTING HEIGHT OF THE BALLOON B !FTER SECOND THE BALLOONS HEIGHT IS SO ONE POINT ON THE LINE IS 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M S D M 4HE RULE IS F S X D X B 4HERE ARE SECONDS IN MINUTES 7HEN X F S X D X F S D S D F S D !FTER MINUTES THE BALLOONS HEIGHT WILL BE FEET 4HE BALLOON WILL HAVE CLIMBED FEET A ,OCATE TWO POINTS &IND THE SLOPE M Y Y ??????? M ??????? X X 3UBSTITUTE M AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR B F S X D MX B S D B B B 4HE RULE IS F S X D X #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED F S X D X F S D S D F S D 7HEN THE COST TO THE CARPENTER IS THE CUSTOMERS COST IS ! F S X D X F S D S D F S D 4HE YINTERCEPT IS THE TOTAL AMOUNT OF WATER IN THE POOL B )F THE PUMP DRAINS FOR MINUTE THE AMOUNT OF WATER IN THE POOL IS SO ONE POINT ON THE LINE IS S D 3UBSTITUTE B AND THE X AND YVALUES INTO THE EQUATION F S X D MX B AND SOLVE FOR M F S X D MX B M S D M 4HE RULE IS F S T D T WHERE T THE AMOUNT OF TIME IN MINUTES 7HEN T F S T D T F S D S D F S D GALLONS !FTER MINUTES THERE WILL BE GALLONS LEFT IN THE POOL 7HEN THE POOL IS EMPTY F S T D F S T D T T T T 4HE POOL WILL BE EMPTY IN MINUTES S D S D S D ??? ??? ??? OR ?? ?? S ??? D S D ??? ??? ??? ??? ??? S D S D ????? ?? ??? ? ? ??? ??? ??? ??? q ^ q ^ q q ^ ^ (OLT -C$OUGAL -ATHEMATICS F S X D q S X D 0!'%3 n 4HINK AND $ISCUSS 0OSSIBLE ANSWER 4HE CURVES HAVE THE SAME BASIC SHAPE BUT THEY ARE REFLECTIONS OF EACH OTHER OVER THE YAXIS 4HE CURVE IN AN EXPONENTIAL GROWTH GRAPH GOES UP AND TO THE RIGHT BUT THE CURVE IN AN EXPONENTIAL DECAY GRAPH GOES DOWN AND TO THE RIGHT Y X F TX E %XERCISES F S X D X X X F TX E ?? ?? F S X D ?? q X X F TX E ?? ?? S D F S X D q ?? X F TX E ??? ??? ??? ??? X Y / F S X D q X X F TX E ?? ?? ?? ??? F S X D q $!4% X %$)4%$ "9 BLACKLINE .%43 MOD ( #&" X %#&"+ ',(" &"!#'! *%#&"+ %"%' %$",")' #% ') "!" $ #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED .%43 V COMPLEX GREYSCALE COLOR Y 4)-% F TX E ONLY ?? ALTERED COMPLEX S D CREATED A R F SX D A q R X F S X D q X HOURS TENHOUR INTERVALS SO FIND F S D S D F q F S D 4HE MASS OF THE COLONY AFTER HOURS IS ') %$",")' G &"!#'! A MG R ?? X X S D F X A q R ( #&" #% %#&"+ *%#&"+ X ?? S D F X q "!" $ %"%' ',(" 4HERE ARE S D MIN IN HOURS 4HERE ARE ONEHUNDRED MINUTE INTERVALS IN H SO FIND F S D F S D q ?? -4%?#?4%#? 4%#( !24 &),% D y F S (27 #534/-%2 .5-"%2 4HERE ARE */" APPROXIMATELY MG REMAINING AFTER #3 HOURS $!4% #2%!4%$ "9 SIMPLE F TX E X F S X D q X X S D (OLT -C$OUGAL -ATHEMATICS ' " F S X D S D X X F TX E S D F S X D ?? A R F SX D A q R X F S X D q X YEARS SIX YEAR INTERVALS SO FIND F S D F S D q F S D 4HE PREDICTED POPULATION OF BIRDS WILL BE A MG R ?? F SX D A q R X X F S X D q ?? 4HERE ARE THIRTY YEAR INTERVALS IN '#,4 YEARS SO FIND F S D 4%#( !24 &),% ? ? (27 S D F q #534/-%2 */" .5-"%2 JH S D F #2%!4%$ "9 $!4% 4HERE WILL BE APPROXIMATELY MG REMAINING %$)4%$ "9 $!4% AFTER YEARS 4)-% F S X D X CREATED ONLY ALTERED .%43 F S D .%43 ?? S D F PLACE CHECKMARK 2%6)3)/. F S D SIMPLE MOD COMPLEX V COMPLEX ?? BLACKLINE GREYSCALE COLOR '#,4 4%#( S X D X !24 F&),% ????? (27 F S D #534/-%2 */" .5-"%2 F S D JH #2%!4%$ "9 $!4% F S D ????? %$)4%$ $!4% "9????? ????? 4)-% Y X / S D X X F TX E ??? ?? Y S D X / ?? ??? S D F S X D ?? X X F TX E ?? CREATED F S X D .%43 X ONLY ALTERED .%43 F S D ????? PLACE CHECKMARK 2%6)3)/. F S D COMPLEX V COMPLEX S D MOD FSIMPLE ????? BLACKLINE GREYSCALE COLOR F S X D q X S S S S Y X F TX E X F S X D q X X F TX E Y X / D D D D X F S X D q ?? ? ? S D F q ! F S D q ?? F S D q ?? (* &%#-#*( S D S D '#"$(" A F S X)D$'# A q R X $& &$'#, +&$'#, q R #"# % (-)# &#&( R R F SX D q X S D S D S D S D A A F SX D A q R X F SX D A q R X q R q R R R ?? R R X F SX D q X ? ? F SX D S D 4%#( !24 &),% '#,4 (27 #534/-%2 #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED #2%!4%$ "9 %$)4%$ "9 JH */" .5-"%2 $!4% (OLT -C$OUGAL -ATHEMATICS $!4% 4)-% A R F SX D q X X Y F TX E ?? ?? S D X !FTER STARTING AT MG THERE IS MG LEFT AFTER HOURS AND MG LEFT AFTER HOURS 3INCE q ?? AND q ?? THE HALFLIFE IS HOURS HOURS X F S X D q ?? WHERE X IS THE NUMBER OF HOUR INTERVALS A R ?? F SX D A q R X X F S X D q ?? 4HERE ARE THREEHOUR INTERVALS IN HOURS SO FIND F S D F S D q ?? F S D 4HERE WILL BE MG OF ACETAMINOPHEN AFTER HOURS ???? 4HERE WILL BE OF THE ORIGINAL DOSE IN THE BODY AFTER HOURS S D S D A R ?? X F S X D ?? X F TX E S D Y / ?? ??? ??? X 5SE THE FUNCTION F S X D A q R X 4HE COMMON RATIO IS ?? AND F S D $IVIDE HOURS BY HOURS TO FIND THE NUMBER OF HALFLIVES X 4HUS F S D ?? MG 4HE ELAPSED TIME BETWEEN NOON AND 0- IS HOURS $IVIDE HOURS BY HOURS TO FIND THE NUMBER OF HALFLIVES FOR THE FIRST SOFT DRINK A R SO X ??? "ECAUSE WE ARE USING F S X D q X ??? Y X F TX E HALFLIVES R ?? 4HE AMOUNT OF CAFFEINE IN THE DRINK -4%?#?4%#? IS MG SO A 4%#( !24 &),% F SX D A q R X (27 #534/-%2 */" .5-"%2 ??? ??? ? ? F q #3 #2%!4%$ "9 $!4% $!4% %$)4%$ "9 F ??? X 4)-% F ??? MG / ONLY ALTERED .%43 CREATED .%43 4HE ELAPSED TIME BETWEEN 0- AND 0- V HOURS COMPLEX MOD IS COMPLEX SIMPLE HOURS $IVIDE BY HOURS TO FIND THE NUMBER OF HALFLIVES FOR THE SECOND SOFT DRINK COLOR GREYSCALE BLACKLINE 3INCE THE EXERCISE IS ASKING FOR THE PERCENT OF THE -4%?#?4%#? CURRENT THAT IS LEFT AND PERCENT IS A NUMBER OUT OF ?? SO X ?? "ECAUSE WE ARE USING !24 &),% 4%#( LET THE INITIAL STRENGTH OF THE CURRENT BE (27 ? ? HALFLIVES 4HE AMOUNT OF CAFFEINE IN THE DRINK #534/-%2 */" R.5-"%2 A R ?? #3 #2%!4%$ "9 $!4% IS MG SO A X F SX D A q R ?? X %$)4%$ "9 $!4% F ?? ?? F S X D q ?? 4)-% ?? S D F 4HERE ARE TWO POINT FIVECREATED MILLISECOND ONLY ALTERED .%43 .%43 INTERVALS IN SECONDS SO FIND F S D ?? MG F SIMPLE MOD V COMPLEX COMPLEX F S D q ?? MG MG MG BLACKLINE GREYSCALE COLOR F S D 4HUS ABOUT MG OF CAFFEINE PRESENT AT 4HERE WILL BE APPROXIMATELY REMAINING 0- AFTER MILLISECONDS # A R ?? X !T TIME THERE WAS MG PRESENT IN THE BODY F SX D A q R X MG F S D q ?? F S D 4HERE WILL BE GRAMS REMAINING S D S D S D S D S D S D S D S D S D S D S D S D #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED (OLT -C$OUGAL -ATHEMATICS F S X D X F S D F S D F S X D X X 6 ??QR H R H ? 6 ?QS D 6 y MM 6 ??QR H D R H ? 6 ?QS D 6 y FT X F TX E X X / X X F TX E 4HE PROBABILITY OF ROLLING AN ODD NUMBER WITH ONE DIE IS ?? ?? 4HE PROBABILITY OF ROLLING AN ODD NUMBER ON THE FIRST DIE AND THE SECOND DIE IS ?? ?? ?? 4HE PROBABILITY OF ROLLING A NUMBER LESS THAN IS ?? OR ?? 4HE PROBABILITY OF ROLLING A NUMBER LESS THAN ON BOTH DIE IS ?? ?? ?? Y !24 &),% ' #534/-%2 #2%!4%$ "9 %$)4%$ "9 CREATED 2%6)3)/. 4HE BALL REACHES A MAXIMUM HEIGHT OF FEET AND STAYS IN THE AIR FOR SECONDS SIMPLE F S X D X X 0!'%3 n 4HINK AND $ISCUSS 0OSSIBLE ANSWER 4HE GRAPH OF F S X D X HAS THE SAME SHAPE AS THE GRAPH OF F S X D X BUT IT IS TRANSLATED UP UNIT 3O THE YINTERCEPT IS INSTEAD OF 0OSSIBLE ANSWER )T IS A SMOOTH CURVE WITH LINE SYMMETRY )T IS NARROWER AT THE BOTTOM AND IT CONTINUES TO GET WIDER AS XVALUES GET FARTHER AWAY FROM X F TX E .%4 BLACKLINE Y X / F S X D X %XERCISES F S X D X X F TX E X F TX E #534/-%2 X / #2%!4%$ "9 %$)4%$ "9 CREATED SIMPLE BLACKLINE F S X D X Y X F TX E -4%?#?4%#? !24 &),% " (27 */" .5-" #534/-%2 #3 #2%!4%$ X"9 $!4% / %$)4%$ "9 $!4% 4)-% )+ '&$.$+) CREATED .%43 ONLY ALTERE ($ #%)# .%4 2%6)3)/. F S X D X F TX E !24 &),% ' X Y *!%($ %' $#$!& '%($- SIMPLE ,'%($-MOD BLACKLINE '$') ).*$ COMPLEX GREYSCALE !24 &),% ' #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED -ATHEMATICS (OLT -C$OUGAL #534/-%2 #2%!4%$ "9 %$)4%$ "9 X X F TX E F S X D X X X S D S D LIE ON THE XAXIS X X F S X D X X 4HE BEACON IS FEET HIGH WHEN IT IS RELEASED 4HE BEACON HITS THE WATER AFTER SECONDS F SX D X F S D S D F S D F S D F S X D ??X F S D ?? S D F S D ?? S D ? S D F ? S D F SX D F S D F S D F S D F TX E F S X D X X X F SX D X S F D S D F S D F S D F TX E S D S D LIE ON THE XAXIS X X F S X D X X X F S X D ?? S D F S D ?????? ??? F S D F S D ??? #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED F TX E S D S D LIE ON THE XAXIS X X X X S D S D S D S D F S X D X X F S D S D S D F S D S D F S D S D X X F TX E S D S D LIE ON THE XAXIS X X (OLT -C$OUGAL -ATHEMATICS F S X D QX A F S X D X X F S D S D S D F S D S D S D F S D S D S D F S D S D S D F S D S D S D B )N PART A THE HIGHEST SALES WERE WHICH WAS WHEN X 3O SEVEN PRICE REDUCTIONS WILL RESULT IN THE HIGHEST SALES F S X D QX QX ???? Q X ^ ???? Q X X q 4HE RADIUS WOULD BE APPROXIMATELY FEET F S T D T T F S D S D S D y F S D S D S D y F S D S D S D y !T AND SECONDS THE AIRPLANE IS AT FT FT AND FT 3INCE THE NUMBERS ARE INCREASING THE AIRPLANE IS FLYING UP A F S T D T T F S D S D S D F S D S D S D F S D S D S D F S D S D S D F S D S D S D F S D S D S D F S D S D S D F S X D X X F S D S D S D F S D S D S D F S D S D S D F S D S D S D 4HE HIGHEST PROFIT IS WHEN X " F S X D S X D X B 4HE ROCKET IS AT ITS HIGHEST POINT AT T SECONDS WHEN THE ROCKET IS FT HIGH C .O POSSIBLE ANSWER 4HE HIGHEST POINT OF THE GRAPH IS SO THE ROCKET REACHES A MAXIMUM HEIGHT OF FEET D 4HE ROCKET IS BACK AT A HEIGHT OF AT T SECONDS SO IT TAKES SECONDS FOR THE ROCKET TO LAND Y F TX E T 0OSSIBLE ANSWER 4HE FUNCTION F S X D X WILL GROW MORE QUICKLY AS X GETS LARGER &OR EXAMPLE WHEN X IS BUT IS ONLY F T F S D 4HE OBJECT REACHES THE GROUND SECONDS AFTER IT WAS DROPPED A FEATHER ! FEATHER WOULD TAKE LONGER TO REACH THE GROUND BECAUSE OF AIR RESISTANCE WHEREAS A ROCK WOULD PROBABLY REACH THE GROUND IN LESS THAN SECONDS SIMPLE #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED BLACKLINE .%43 GREYSCALE X 4HE GRAPH HAS NO XINTERCEPTS # F S T D T T #HECK EACH VALUE OF T TO FIND F S T D #HOICE ! CAN BE ELIMINATED BECAUSE AT TIME THE TENNIS BALL HASNT BEEN THROWN YET F S D S D S D 4HE TENNIS BALL IS BACK AT HEIGHT AFTER SECONDS ONLY ALTERED MOD / 4HE GRAPH OF A LINEAR FUNCTION IS A STRAIGHT LINE 4HE GRAPH OF A QUADRATIC FUNCTION IS A PARABOLA 4HE 4%#( LINEAR FUNCTION EQUATION A VARIABLE TO THE !24CONTAINS &),% -4%?#?4%#? F S X D X X (27 FIRST POWER 4HE QUADRATIC FUNCTION EQUATION CONTAINS #534/-%2 */" .5-"%2 X A VARIABLE SQUARED ! LINEAR FUNCTION HAS #3 THE FORM #2%!4%$ "9 $!4% IN ???? IN ???? F S X D MX B ! QUADRATIC FUNCTION HASFPTHE FORM %$)4%$ "9 X $!4% FT F S X D AX BX C X FT 4)-% CREATED COMPLEX #534/-%2 #2%!4%$ " %$)4%$ "9 CREATED IN IN ???? ???? X FT X FT .%43 V COMPLEX COLOR !24 &),% ' (OLT -C$OUGAL -ATHEMATICS . 2%6)3)/. SIMPLE BLACKLINE ? F S X D ? X X IN IN ?????? ???? X FT X FT IN ????? IN ???? X FT X FT 0UT THE DATA IN NUMERICAL ORDER ??????? &IND THE MEDIAN &IND THE MEDIAN OF EACH HALF OF THE DATA ??????? ??????? ?? ?? 0UT THE DATA IN NUMERICAL ORDER ??????? &IND THE MEDIAN &IND THE MEDIAN OF EACH HALF OF THE DATA 4HINK AND $ISCUSS 0OSSIBLE ANSWER !S ONE QUANTITY INCREASES THE OTHER WILL DECREASE 4HEN CHECK TO SEE THAT THE PRODUCT OF THE XVALUES AND YVALUES IS A CONSTANT NUMBER ?? ?? %XERCISES S D S D 4HE PRODUCT IS NOT ALWAYS THE SAME 4HE RELATIONSHIP BETWEEN SOCCER BALLS PRODUCED AND TIME IS NOT AN INVERSE VARIATION S D S D S D S D S D XY 4HE PRODUCT IS ALWAYS THE SAME 4HE RELATIONSHIP BETWEEN PAINTING TIME AND NUMBER OF WORKERS IS AN INVERSE VARIATION ? F S X D ? X X Y Y ?? ?? ?? ?? F S X D ??? X X ?? ?? X / Y ?? ? ? ?? ?? ?? ?? ?? ?? Y ?? ? ? ? ? ? ? ?? ?? ?? ?? 9OU CAN&),% SEE FROM THE TABLE THAT XY S D 4%#( '?#?,?4 !24 )F THE RESISTANCE (27 SO Y ??? IS OHMS THEN THE X #534/-%2 */" .5-"%2 ??? CURRENT WILL BE Y AMPS JH $!4% #2%!4%$ "9 S D S D S D S D %$)4%$ "9 $!4% S D 4)-% XY CREATED .%43 ONLYRELATIONSHIP ALTERED .%43 4HE PRODUCT IS ALWAYS THE SAME 4HE BETWEEN THE SPEED OF THE CAR AND THE TIME IS AN PLACE CHECKMARK 2%6)3)/. INVERSE VARIATION SIMPLE MOD COMPLEX V COMPLEX BLACKLINE #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED K ?? F S X D ??? X X 0!'%3 n ?? Y GREYSCALE COLOR (OLT -C$OUGAL -ATHEMATICS F S X D ??? X S D S D 4HE PRODUCT IS NOT ALWAYS THE SAME 4HE RELATIONSHIP BETWEEN THE MILES BICYCLED AND THE TIME IS NOT AN INVERSE VARIATION ? F S X D ? X X ?? ?? Y ?? ?? ?? ?? F S X D ??? X X Y ??? ?? ?? ?? ?? ?? ?? ??? F S X D ??? X X ?? ?? Y ??? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ??? S D 9OU CAN SEE FROM THE TABLE THAT SO )F THE VOLUME IS LITERS THEN ??? Y THE PRESSURE X " ATM WILL BE Y ??? ? XY S D SO Y ? X S D SO Y ??? XY )+ '&$.$+) X X Y ?? ?? ?? ?? ? ? ? ? ? ? ? ? XY S D SO Y ??? ($ #%)# X *!%($ %' '%($,'%($S D XY SO K $#$!& '$') BH S D SO B ).*$ ???? H ???? B 7HEN THE HEIGHT IS CM THE BASE IS CM A 9OU CAN SEE FROM THE TABLE THAT XY S D SO Y ??? X B 7HEN THE ACCELERATION IS MS THE MASS IS Y ??? #! 4HE MASS IS KG S D SO XY AND Y ??? X *, ('%/%,* )F THE INTEREST RATE IS OR THEN Y ??????? )%!$&*$ -R !NDERSON MUST DEPOSIT +"&)% &( AT (&)%. -(&)%. INTEREST TO EARN IN INTEREST IN YEAR %$%"' */+% (%(* #HECK STUDENTS WORK 0OSSIBLE ANSWER (OW TO DIVIDE JELLYBEANS AMONG A DIFFERENT NUMBER OF STUDENTS 0OSSIBLE ANSWER )N DIRECT VARIATION THE VARIABLES INCREASE OR DECREASE TOGETHER )T IS OF THE FORM Y KX )N INVERSE VARIATION ONE VARIABLE INCREASES AS THE OTHER DECREASES )T IS OF THE FORM Y ?KX? THE DIAMETER " S D SO X Y OR Y ??? X )F THE DIAMETER IS IN THEN Y ??? 4HE)+ RESISTANCE IS OHMS FOR A IN DIAMETER WIRE '&$.$+) *!%($ #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED WITH THE SQUARE OF 4HE RESISTANCE VARIES INVERSELY $#$!& %' '%($- ($ #%)# ,'%($- '$') (OLT).*$ -C$OUGAL -ATHEMATICS )+ *!%( $#$!& F S X D X $ XY S D SO K X XY S D SO Y ??? X AND X 7HEN Y ??? X ? ? ? ? X ??X X ??X X ?? ??X ?? ??? ??X ??? ??? X P P P K K K ??? X X X X F SX D X / S D D !24 &),% - #534/-%2 #2%!4%$ "9 X "9 %$)4%$ / CREATED X X F S X D X X X ,INEAR M B F S X D ??X ??X ,INEAR M ?? B )DENTIFY THE YINTERCEPT B ,OCATE ANOTHER POINT S D F S X D MX B M S D M M F S X D MX B F S X D X Y F S X D ?? F S X D X 4HE VARIABLE IS RAISED TO AN EXPONENT OTHER THAN SO THE FUNCTION IS NOT LINEAR )F +AYO WORKS HOURS OF OVERTIME SHE EARNS SO B )F +AYO WORKS HOUR OF OVERTIME SHE EARNS SO S D IS ANOTHER POINT ON THE GRAPH F S X D MX B M S D M F S X D MX B F S X D X F S D S D F S X D X F S X D q X 2%!$9 4/ '/ /. 0!'% S Y F SX D ?? ?? .%43 -4% SIMPLE F SX D ?? ?? ?? ?? Y !24 &),% BLACKLINE #534/-%2 #2%!4%$ "9 %$)4%$ "9 CREATED .%43 X SIMPLE / M BLACKLINE F S X D A q R X -4% 3INCE THE ACCOUNT DOUBLES EVERY YEARS !24 R &),% #534/-%2 3INCE HE BEGINS WITH A F S X D q X #2%!4%$ "9 )N YEARS THERE WILL BE EIGHTYEAR %$)4%$ "9 INTERVALS F S D q F S X D q X CREATED .%43 F S X D X Y X F SX D SIMPLE M BLACKLINE X / !24 &),% - #534/-%2 #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED #2%!4%$ "9 (OLT -C$OUGAL -ATHEMATICS %$)4%$ "9 F S X D X X X F SX D Y ?? ? ? ?? ?? X / X X ? F S X D ? X Y X F SX D Y X ?? ?? !24 &),% -4%?#?4%#? #534/-%2 4%#( (27 */" .5-"%2 345$9 '5)$% 2%6)%7 0!'%3 n #3 #2%!4%$ "9 $!4% SEQUENCE %$)4%$ "9 $!4% ARITHMETIC SEQUENCE GEOMETRIC SEQUENCE 4)-% D CREATED .%43 ONLY ALTERED .%43 A N A S N DD SIMPLE A MOD V COMPLEX D S COMPLEX S D A BLACKLINE GREYSCALE COLOR 4HE PEBBLE IS FEET FROM THE SURFACE OF THE WATER D !FTER SECONDS THE PEBBLE HITS THE WATER A N A S N DD ? F S X D ? A S D X A S D X Y D ?? ?? ?? ?? ?? ?? ?? A N A S N DD A ?? S D?? ?? ? ? ? ? ??? A S D ?? ???? R N A N A R A q S D ?? ?? R ?? ?? ?? ?? ?? F S X D ??? X A N A R N X Y ? ? q ?? ???? A ?? ? ? R ?? A N A R N ?? D A q S $& A N N "!)&$ ?? A S D % # '" #( S D " #( A" ?? S D A ""$ ! $)% ?? A S D ?? AN N A S D ?? A S D S D A A S D S D #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED %' (OLT -C$OUGAL -ATHEMATICS #" * '% A N S D N N A S D S D A S D S D A S D S D A S D S D ????? A N N N S D A ??????? ?? S D S D ??????? ? A ? S D S D A ??????? ?? S D S D A ??????? ?? S D ?? ?? ?? ?? A N S N D S N D A S S D D S S D D A S S D D S S D D A S S D D S S D D A S S D D S S D D S D X F S X D q ?? X F TX E F TX E ?? ?? F TX E ???? ?? Y X X F TX E 0- 0- !- 0- PEOPLE WATCHED THE VIDEO AFTER HOURS F S X D X X #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED ?? X F S X D q X F TX E F S X D q X X &ROM THE GRAPH B &OR THE POINT FX MX B M M FX X F S X D X 4HE YINTERCEPT IS F S D 4HE LINE PASSES THROUGH S D F S X D MX B M S D M ?? M F S X D ??X &ROM THE GRAPH B &OR THE POINT S D F S X D MX B M S D S D M F S X D 4HE YINTERCEPT IS F S D 4HE LINE PASSES THROUGH S D F S X D MX B M S D S D M F SX D X X F TX E (OLT -C$OUGAL -ATHEMATICS CREATED Y ??? F S X D X / X X F S X D X X X F TX E !24 &),% '?#?3'2?4 (27 #534/-%2 F TX E CREATED 2%6)3)/. %$)4%$ "9 .%43 SIMPLE MOD BLACKLINE COMPLEX GREYSCALE X Y / F TX E X X V COMPLEX Y X / ?? X Y !24 &),% ' #534/-%2 #2%!4%$ " %$)4%$ "9 / ? Y ? X )T WILL TAKE HOURS TO DECORATE IF THERE ARE VOLUNTEERS F TX E X / X COLOR Y #(!04%2 4%34 0!'% !24 &),% '?#?3'2?4 D AN A A S D A A S N DD S D S D 4%#( S D S D D ?? ?? A */" .5-"%2 JH $!4% A A S N DD #2%!4%$ "9 N JH $!4% A S D?? %$)4%$ "9 4)-% A S D?? ?? CREATED .%43 ONLY ALTERED .%43 D A PLACE CHECKMARK 2%6)3)/. REACHES 4HE BALL STAYS IN THE AIR FOR SECONDS AND AN A S N DD A MAXIMUM HEIGHT OF SIMPLE FEET S D S D MOD COMPLEX A V COMPLEX ??? S D A Y X COLOR S D BLACKLINE GREYSCALE A D Y X F TX E A N A S N DD A S D A S D X A R ??? / N A A R N A q A #OPYRIGHT © BY (OLT -C$OUGAL !LL RIGHTS RESERVED COLOR X F S X D X X V COMPL F TX E ONLY ALTERED .%43 ?? PLACE CHECKMARK PLACE CHECK */" .5-"%2 4)-% COMPLEX GREYSCALE JH $!4% ?? Y JH $!4% X #2%!4%$ "9 X MOD .%43 Y 4%#( BLACKLINE X F TX E SIMPLE ONLY ALTERED 2%6)3)/. Y .%43 #534/-%2 (27 (OLT -C$OUGAL -ATHEMATICS CREATED . 2%6)3)/. SIMPLE BLACKLINE X / ?? ??? R ?? ?? A ?? ?? A N A R N A ?? q S D A ?? 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F X ONLY ALTERED .%43 CREATED .%43 -4%?#?4%#? 4%#( !24 &),% F S D ???? SIMPLE MOD COMPLEX V COMPLEX (27 #534/-%2 */" .5-"%2 BLACKLINE COLOR S D ?? FGREYSCALE LF #2%!4%$ "9 $!4% 4HE TRIP WILL TAKE ?? HOURS %$)4%$ "9 $!4% Y #3 #2%!4%$ "9 / (27 #534/-%2 F TX E / %$)4%$ "9 X / F TX E #3 #2%!4%$ "9 F S X D X X X (27 #534/-%2 X -4%?#?4%#? -4%?#?4%#? #534/-%2 (27 #2%!4%$ "9 33 */" .5-"%2 $!4% .%43 ONLY ALTERED MOD COMPLEX GREYSCALE 4%#((OLT -C$OUGAL -ATHEMATICS .%43 V COMPLEX COLOR
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