Name:  ______________________________________  Class:  ______________  Date:  ____________  

Unit 6: Say it with Symbols Investigation 4: Looking Back At Functions

Practice Ace Problems

Directions:  Please  complete  the  necessary  problems  to  earn  a  maximum  of  8  points  according  to  the  chart  below.  Show  all  of  your  work  clearly  and  neatly  for  credit-­‐  which  will  be  earned  based  on  completion  rather  than  correctness.  

I can determine the patterns of change in tables or graphs represented by expressions or equations.

Lesson Practice problems Options Maximum Points

Lesson 1: Looking at Patterns of Change

1, 2, 3

2 Points

Lesson 2: Linear, Exponential, Quadratic Functions

8, 9, 11, 12, 13 5 Points

______/ 7 Points

 

 

 

 

 

 

 

 

 

 

 

 Name:  ______________________________________  Class:  ______________  Date:  ____________  

1. A  pump  is  used  to  empty  a  swimming  pool.  The  equation  w  =  -­‐275t  +  1,925  represents  the  gallons  of  water  w  that  remains  in  the  pool  t  hours  after  pumping  starts.  

 a. How  many  gallons  of  water  are  pumped  out  each  hour?  

   

b. How  many  gallons  of  water  is  in  the  pool  at  the  start  of  pumping?      

c. Suppose  there  are  1,100  gallons  of  water  left  in  the  pool.  How  long  has  the  pump  been  running?  

 

 

d. After  about  how  many  hours  will  the  pool  be  empty?  

 

 

e. Write  an  equation  that  is  equivalent  to  w  =  -­‐275t  +  1,925.  What  information  does  it  tell  you  about  the  situation?  

 

f. Without  graphing,  describe  what  the  shape  of  the  graph  would  look  like  for  the  relationships  between  w  and  t.    

   

 

2. A  new  pump  is  used  to  empty  the  pool  in  Question  1.  The  equation  w  =  -­‐275(2t  –  7)  represents  the  gallons  of  water  w  that  remain  in  the  pool  t  hours  after  pumping  starts.  

 a. How  many  gallons  of  water  are  pumped  out  each  hour?  

   

b. How  many  gallons  of  water  is  in  the  pool  at  the  start  of  pumping?      

c. Suppose  there  are  1,100  gallons  of  water  left  in  the  pool.  How  long  has  the  pump  been  running?  

 Name:  ______________________________________  Class:  ______________  Date:  ____________  

 

d. After  about  how  many  hours  will  the  pool  be  empty?  

 

 

e. Write  an  equation  that  is  equivalent  to  w  =  -­‐275(2t  –  7).  What  information  does  it  tell  you  about  the  situation?  

 

f. Without  graphing,  describe  what  the  shape  of  the  graph  would  look  like  for  the  relationships  between  w  and  t.    

 

3. A  truck  has  a  broken  fuel  gauge.  Luckily,  the  driver  keeps  a  record  of  mileage  and  gas  consumption.  The  driver  uses  the  data  to  write  an  equation  for  the  relationship  between  the  number  of  gallons  of  gas  in  the  tank  g  and  the  number  of  miles  driven  m  since  the  last  fill-­‐up.  

g  =  25  -­‐   𝟏𝟏𝟓m  

a. How  many  gallons  of  gasoline  are  in  a  full  tank?  

 

b. Suppose  the  driver  travels  50  miles  after  filling  the  tank.  How  much  gas  is  left?  

 

 

c. After  filling  the  tank,  how  many  miles  can  the  driver  travel  before  5  gallons  remain?  

 

 

d. After  filling  the  tank,  how  many  miles  can  the  driver  travel  before  the  tank  is  empty?  

 

 

e. How  many  miles  does  the  driver  have  to  travel  in  order  to  use  1  gallon  of  gas?  

 

 Name:  ______________________________________  Class:  ______________  Date:  ____________  

f. In  the  equation,  what  do  the  numbers  25  and   !!"  tell  you  about  the  situation?  

 

 

8. The  tables  below  represent  the  projected  growth  of  certain  species  of  deer.  Use  the  three  tables  to  answer  parts  (a)  –  (c).  

 

a. Describe  the  growth  represented  in  each  table.  Do  any  of  these  patterns  represent  linear,  exponential,  or  quadratic  functions?  Which  ones?  

 

 

b. Write  an  equation  for  each  pattern  that  represents  a  linear  or  exponential  function.  

 

 

c. Does  any  table  show  a  population  of  deer  growing  at  a  rate  of  3%  per  year?  Explain.  

 

 

 

9. The  Department  of  Natural  Resources  is  collecting  data  on  three  different  species  of  animals.  They  find  that  these  species  show  different  patterns  of  population  growth.  They  wrote  the  equations  below  to  represent  the  population  P  of  each  species  after  t  years.  

 

 Name:  ______________________________________  Class:  ______________  Date:  ____________  

a. Describe  what  information  the  numbers  and  variables  represent  in  each  situation.  

Species  1:  

  Species  2:  

  Species  3:  

 

b. Describe  the  pattern  of  growth  for  each  species.  Explain  how  patterns  differ.  

Species  1:  

  Species  2:  

  Species  3:  

 

c. Pick  any  two  species.  After  how  many  years  will  the  population  of  the  two  species  be  equal?  Explain  how  you  got  your  answer.  

 

 

 

 

 

Use  the  four  graphs  to  answer  Exercises  11  –  13.  

 

 Name:  ______________________________________  Class:  ______________  Date:  ____________  

11.  What  graph  represents  a  linear  function?  A  quadratic  function?  An  exponential  function?  

  Linear:         Quadratic:       Exponential:  

 

 

12.  Make  a  table  of  y-­‐values  for  x  =  1  through  6  for  each  function.  

Graph  1     Graph  2     Graph  3  

x   y     x   y     x   y  

1       1       1    

2       2       2    

3       3       3    

4       4       4    

5       5       5    

6       6       6    

 

13.  Write  an  equation  for  each  function.    

  Graph  1:  

  Graph  2:  

  Graph  3:  

   

 

 

Exit Ticket Level of Understanding

After finishing this investigation you should be comfortable doing the following: - Determine the patterns of change in tables or graphs represented by expressions or equations.

 Name:  ______________________________________  Class:  ______________  Date:  ____________