1. Functions and Their Representation
Lesson 1.3

2. What is a Function A relationship between two quantities
Reperesented by:
A table
A formula A =  r2
A description
A graph x 7 2 9 3 y 8 4 5

3. Definition of a Function
Mathematical definition: A set of ordered pairs where no two ordered pairs have the same first element

4. Evaluating Possible Functions
Which is a function?
{(2,3), (4,7), (9,3)} {(2,3), (4,7), (2,9)} {(2,3), (4,7), (9,2)}

5. Function Notation
If we say “R is a function of t” the notation is … R = f(t)
Note: f(t) does not mean f * t

6. Using Function Notation
Suppose we say h(t) = -16t2 +64t
The height of a ball thrown into the air is a function of t, time
We evaluate functions by substituting a value for time into the formula
That is
h(3) = -16* *3
Which evaluates to ???

7. Defining a function on the TI-Calculator
Enter the formula as shown on the command line:
-> is the STO> key

8. Using TI-Calculator Functions
On the entry line enter h(3)
Press <enter>
Try evaluating the function h(t) for different values of t
h(7)
h(-4)
h(x+2)

9. Using TI-Calculator Functions
Graphing the funciton
Go to the Y= screen (♦W)
Enter in the function – you must use x's as the independent variable
Options
Enter function entirely
Reference a previously defined function

10. Using TI-Calculator Functions
Check the range of values with the table feature, ♦Y
Change the increment of the first column, use F2
Change start, increment value
Viewing resultant values helps set window for graph

11. Using TI-Calculator Functions
Go to setup window with ♦E
Set max and min values
Go to graph with ♦R
Height as a function of time
Note, this is not a picture of the path of the object
Time

12. Assignment
Lesson 1.3
Page 38
Exercises
1 – 77 EOO