Functions and Their Representation Lesson 1.3

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

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

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)}

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

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*32 + 64*3 Which evaluates to ???

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

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)

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

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

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

Assignment Lesson 1.3 Page 38 Exercises 1 – 77 EOO