Functions as Mathematical Models PDF

ATENEO DE ILOILO MATHEMATICS SANTA MARIA CATHOLIC SCHOOL S E N IO R H IG H S C H O O L Fu n ct io n s a s Ma t h em a t ica l Mo d el Unit 1....

ATENEO DE ILOILO MATHEMATICS SANTA MARIA CATHOLIC SCHOOL S E N IO R H IG H S C H O O L Fu n ct io n s a s Ma t h em a t ica l Mo d el Unit 1.1:Ma t h e m a t ic a l Mo d e l Ob je c t iv e s : re p re s e n ts re a l- life s itu a tio n s u s in g p ie c e wis e fu n c tio n s ; s o lve s p ro b le m s in vo lvin g fu n c tio n s ; d e te rm in e s th e c h a ra c te ris tic s o f a fu n c tio n in te rm s o f its d o m a in a n d ra n g e ; a n d g ra p h s p ie c e wis e fu n c tio n s  FLOW OF SESSION Ma t h e m a t ic a l Min i Ex it C a r d Mo d e l P e r fo r m a n c e Ta s k W e lc o m e t o Ta t a y Te xt ile In local t - s h irt re ta il s to re , th e o wn e r c h a rg e s Ph p 15 5 p e r t- s h irt fo r o rd e rs o f 5 0 o r fe we r T- s h irts , Ph p 15 0 p e r T- s h irt fo r o rd e rs o f 75 o r fe we r b u t m o re th a n 5 0 T- s h irts , a n d Ph p 14 5 p e r T- s h irt fo r o rd e rs o f m o re th a n 75 T- s h irts. C re a te a fu n c tio n th a t m o d e ls th is s itu a tio n. W e lc o m e t o Ta t a y Te xt ile W h a t is Ma t h e m a t ic a l Mo d e ls ? it is a mathematical description o f a re a l- wo rld s itu a tio n. Sc e n a rio 1: J e e p n e y Fa re A jeepney ride costs Php 14.00 for th e firs t 4 kilo m e te rs , a n d e a c h a d d itio n a l in te g e r kilo m e te r a d d s Ph p 1.20 to th e fa re. Us e a p ie c e wis e fu n c tio n to re p re s e n t th e je e p n e y fa re in te rm s o f th e d is ta n c e d in kilo m e te rs. Le t 's En g a g e Case Study Analysis Th e re w ill b e 4 g ro u p s a n d e a c h g ro u p w ill c h o o s e a re p re s e n ta tive to p ic k a p ie c e o f p a p e r ( C a s e ). Ea c h g ro u p will b e g ive n 20 m in u te s to d o th e ta s k a n d th e y w ill p re s e n t th is in fro n t. Le t 's En g a g e Case Study Analysis C a s e Stu d y 1 C a s e Stu d y 2 C a s e Stu d y 3 C a s e Stu d y 4 Le t 's En g a g e Case Study Analysis C a s e Stu d y 1 A la n d s c a p e r re n ts a w o o d c h ip p e r fo r 4 d a ys. Th e re n ta l c o m p a n y c h a rg e s Ph p 5 ,0 0 0 fo r th e firs t d a y a n d Ph p 2,5 0 0 fo r e a c h a d d itio n a l d a y. 1. Write a fu n c tio n th a t re p re s e n ts th e re la tio n s h ip b e tw e e n th e n u m b e r x o f d a ys a n d th e to ta l c o s t y ( in p e s o s ) o f re n tin g th e c h ip p e r. 2. Gra p h th e g ive n fu n c tio n. 3. De s c rib e th e d o m a in a n d ra n g e. Le t 's En g a g e Case Study Analysis C a s e Stu d y 2 A vid e o ke m a c h in e c a n b e re n te d fo r P1,0 0 0 fo r th re e d a ys , b u t fo r th e fo u rth d a y o n w a rd s , a n a d d itio n a l c o s t o f P4 0 0 p e r d a y is a d d e d. 1. Write a fu n c tio n th a t re p re s e n t th e c o s t o f re n tin g a vid e o ke m a c h in e a s a p ie c e w is e fu n c tio n o f th e n u m b e r o f d a ys it is re n te d a n d p lo t its g ra p h. 2. Gra p h th e g ive n fu n c tio n. 3. De s c rib e th e d o m a in a n d ra n g e. Le t 's En g a g e Case Study Analysis C a s e Stu d y 3 Th e c o s t o f h irin g a c a te rin g s e rvic e to s e rve fo o d fo r a p a rty is P15 0 p e r h e a d fo r 20 p e rs o n s o r le s s , P130 p e r h e a d fo r 21 to 5 0 p e rs o n s , a n d P110 p e r h e a d fo r 5 1 to 10 0 p e rs o n s. Fo r m o re th a n 10 0 p e rs o n s , th e c o s t is a t P10 0 p e r h e a d. 1. Write a fu n c tio n th a t re p re s e n t th e to ta l c o s t a s a p ie c e w is e fu n c tio n o f th e n u m b e r o f a tte n d e e s o f th e p a rty. 2. Gra p h th e g ive n fu n c tio n. 3. De s c rib e th e d o m a in a n d ra n g e. Le t 's En g a g e Case Study Analysis C a s e Stu d y 4 Wh e n kim c h i is m a d e , it is in itia lly fe rm e n te d fo r th e firs t 3 d a ys a t a te m p e ra tu re o f 𝟕𝟕𝟎𝟎°𝑭𝑭 a n d th e n im m e d ia te ly m o ve d to a te m p e ra tu re o f 𝟓𝟓𝟎𝟎°𝑭𝑭 fo r a n o th e r 3 d a ys a fte r w h ic h it is p u t in a 𝟑𝟑𝟓𝟓°𝑭𝑭 fo r 6 d a ys. 1. Mo d e l th e Fa h re n h e it te m p e ra tu re , 𝑭𝑭, o f th e kim c h i o ve r tim e , 𝒕𝒕, in d a ys u s in g a fu n c tio n. 2. Gra p h th e g ive n fu n c tio n. 3. De s c rib e th e d o m a in a n d ra n g e.  FLOW OF SESSION Ma t h e m a t ic a l Min i Ex it C a r d Mo d e l P e r fo r m a n c e Ta s k Unit 1.1:Ma t h e m a t ic a l Mo d e l Ob je c t iv e s : re p re s e n ts re a l- life s itu a tio n s u s in g p ie c e wis e fu n c tio n s ; s o lve s p ro b le m s in vo lvin g fu n c tio n s ; d e te rm in e s th e c h a ra c te ris tic s o f a fu n c tio n in te rm s o f its d o m a in a n d ra n g e ; a n d g ra p h s p ie c e wis e fu n c tio n s