1. ©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
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2. 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.  
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3. ©Evergreen Public Schools 2010
Function Notation The notation G(x) is read … “G of x” it means “G is a function of x”
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4. ©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
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5. ©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”
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6. ©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”
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7. ©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”
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8. ©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”
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9. ©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
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10. ©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
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11. ©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
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12. ©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
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13. ©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
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14. ©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
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15. ©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
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16. ©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) =
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17. ©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) =
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18. ©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) =
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19. ©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
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20. Work the next problem by yourself.
Be prepared to share.
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21. ©Evergreen Public Schools 2010x
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.
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22. ©Evergreen Public Schools 2010x
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.
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23. ©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
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24. ©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
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25. ©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
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26. ©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
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27. ©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
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28. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5 x
h(x)
J(x)
m(x)
Z(x) 2 7 1 -5 3 4 -2 9 5 16
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29. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 2 x
h(x)
J(x)
m(x)
Z(x) 2 7 1 -5 3 4 -2 9 5 16
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30. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = x = 2 or x = 4 x
h(x)
J(x)
m(x)
Z(x) 2 7 1 -5 3 4 -2 9 5 16
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31. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 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
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32. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 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) = x = 3
h(x) = -2
J(x) = 16
Challenge:
h(x) = J(x)
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33. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 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) = x = 3
h(x) = x = 5
J(x) = 16
Challenge:
h(x) = J(x)
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34. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 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) = x = 3
h(x) = x = 5
J(x) = x = 5
Challenge:
h(x) = J(x)
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35. ©Evergreen Public Schools 2010
How does this Function Notation work with Tables?
Given an output…
J(x) = 1 x = 2
m(x) = x = 5
Z(x) = 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) = x = 3
h(x) = x = 5
J(x) = x = 5
Challenge:
h(x) = J(x) x = 3
What other equation can be formed?
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36. Work the next problem by yourself.
Be prepared to share.
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37. ©Evergreen Public Schools 2010x
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.
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38. ©Evergreen Public Schools 2010x
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
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39. ©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
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40. ©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!
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41. ©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
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