©Evergreen Public Schools 2010 Launch A portion of the graph of f(x) is recorded in the table. Fill in the missing part of each coordinate point. ( ____ , 1 ) ( 3 , ____ ) x Z(x) f(x) -3 3 -20 -1 -13 1 -6 7 5 18 8 2 15 ©Evergreen Public Schools 2010

2-7 Solving Equations With Algebra Tiles powerpoint Learning Target I can read Function Notation to evaluate expressions or solve equations using a table of values. How is a table of values like a graph? M1.2.B  Represent  a  function  with  a  symbolic  expression,  as  a  graph,  in  a  table,  and  using  words,  and  make  connections  among  these  representations.   M1.2.C   Evaluate  f(x)  at  a  (i.e.,  f(a))  and  solve  for  x  in  the  equation  f(x)  =  b.   ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Function Notation The notation G(x) is read … “G of x” it means “G is a function of x” ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? x 2 3 4 5 In this presentation each function is defined by the table. That means these are the only input (x) values. Usually tables are just a small subset of the values connected by the relationship. Inputs ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? x h(x) 2 7 3 4 1 5 -2 Inputs Output values for a new function “h” ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? x h(x) J(x) 2 7 1 3 4 9 5 -2 16 Inputs Output values for a new function “J” ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? x h(x) J(x) m(x) 2 7 1 -5 3 4 -2 9 5 16 Inputs Output values for a new function “m” ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 Inputs Output values for a new function “Z” ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… Z(3) = h(2) = J(4) = Challenge: J(1) = Work with a partner ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… Z(3) = 1 h(2) = J(4) = Challenge: J(1) = ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… Z(3) = 1 h(2) = 7 J(4) = Challenge: J(1) = ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… Z(3) = 1 h(2) = 7 J(4) = 9 Challenge: J(1) = ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an input… h(5) = -2 m(4) = 1 J(2) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… Z(3) = 1 h(2) = 7 J(4) = 9 Challenge: J(1) = Undefined ©Evergreen Public Schools 2010

Work the next problem by yourself. Be prepared to share. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 x T(x) w(x) -3 11 -25 -1 7 -9 1 3 5 -5 T(5) = w(7) = T(-1) = w(-9) = Work by yourself. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 x T(x) w(x) -3 11 -25 -1 7 -9 1 3 5 -5 T(5) = w(7) = T(-1) = w(-9) = -5 -25 7 undefined Time to share. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Debrief Quick Write… Describe how you would explain to a friend or parent the process for finding the answer for P(5) given a table of values for P(x). You may be asked to present your description ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… m(x) = -2 h(x) = -2 J(x) = 16 Challenge: h(x) = J(x) Work with a partner ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… m(x) = -2 x = 3 h(x) = -2 J(x) = 16 Challenge: h(x) = J(x) ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… m(x) = -2 x = 3 h(x) = -2 x = 5 J(x) = 16 Challenge: h(x) = J(x) ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… m(x) = -2 x = 3 h(x) = -2 x = 5 J(x) = 16 x = 5 Challenge: h(x) = J(x) ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 How does this Function Notation work with Tables? Given an output… J(x) = 1 x = 2 m(x) = 4 x = 5 Z(x) = 2 x = 2 or x = 4 x h(x) J(x) m(x) Z(x) 2 7 1 -5 3 4 -2 9 5 16 You give it a try… m(x) = -2 x = 3 h(x) = -2 x = 5 J(x) = 16 x = 5 Challenge: h(x) = J(x) x = 3 What other equation can be formed? ©Evergreen Public Schools 2010

Work the next problem by yourself. Be prepared to share. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 x T(x) w(x) -3 11 -25 -1 7 -9 1 3 5 -5 T(x) = 11 w(x) = -25 T(x) = -9 w(x) = -9 T(x) = w(x) Work by yourself. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 x T(x) w(x) -3 11 -25 -1 7 -9 1 3 5 -5 T(x) = 11 w(x) = -25 T(x) = -9 w(x) = -9 T(x) = w(x) x = -3 x = - 3 or x = 7 x = 7 x = - 1 or x = 5 Time to share. x = 3 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Debrief Quick Write… Describe how you would explain to a friend or parent the process for finding the answer to the statement P(x) = 5 given a table of values for P(x). You may be asked to present your description ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 2-7 Solving Equations With Algebra Tiles powerpoint Learning Target Did you hit the target? I can read Function Notation to evaluate expressions or solve equations using a table of values. 5 3 1 2 4 M1.2.B  Represent  a  function  with  a  symbolic  expression,  as  a  graph,  in  a  table,  and  using  words,  and  make  connections  among  these  representations.   M1.2.C   Evaluate  f(x)  at  a  (i.e.,  f(a))  and  solve  for  x  in  the  equation  f(x)  =  b.   Rate your understanding of the target from 1 to 5. 5 is a bullseye! ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Ticket Out x Z(x) f(x) -3 3 -20 -1 -13 1 -6 7 5 18 8 2 15 Evaluate f(1) Solve Z(x) = 3 ©Evergreen Public Schools 2010