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Section 1 - Functions

This version was saved 16 years, 4 months ago View current version     Page history
Saved by PBworks
on December 19, 2007 at 5:23:44 pm
 

Meg Modzelewski

Kristin Huntington

 

Functions

 

Relation-a set of ordered pairs

                     {(1,5),(-2,3)}

Function-relation in Which every input (x) has only one output Cy)

              (does the x repeat Itself? If so, it's not a function)

vertical line test- If line crosses more than once, then It is not a function

 

Function Notation -f(x)

                             - reads as F of X

 

 

 

Ex. Which equation Represent y as a function of X?

      a.)   x2+ y= 1

                    y= -x2 +1

Yes it is a function because it passes the vertical line test.

 

       b.)  -x+Y2 =1

                  Y2  = x+1

                  Y2 =\sqrt{x+1}

                   y  = ±\sqrt{x+1}

 

 

 

 

Not a function because it does not pass the vertical line test.

      *if solve for y and get 2 equations, its not a function*

 

 

 

 

ex) f(x)= -x2+4x+1   find: f(2), h(x+1)

      f(2)= -22+4(2)+1

           = -4+8+1

           = 5

      h(x+2) = -Formula + 4(x+2) +1

                 = -(x2+4x+4)+4x+8+1

                 = -x2-4x-4x+4x+8+1

                 = -x2+5

 

 

Piece-wise Function 

 

f(x)={x/2+1, x<1

       {3x=2, x>1

 

a) f(0)= 0/2 +1

         = 1

b) f(2)= 3(2)+2

          = 8

 

 

Domain- x values

 

f(x)=\sqrt x   D:[0,)

 

f(x)= 1/(x2-4)     D:(-,), x≠ ±2

                              R, x≠ ±2

                              (-, -2)U(-2,2)U(2,)

 

Domain "Problems"

  1. radical, inside ≥ 0 and solve --> domain

  2. variables in denominator of fraction, denominator=0 and solve -->bad numbers

 

 

ex) f(x)= -2x +4   Find f(x+h)-f(x)

                                         h

 

      f(x+h)= -2(x+h)+4

                   -2x-2h+4

          f(x)= -2x+4

 

 

     -2x-2h+4-(-2x+4)    

                  h

 

     -2x-2h+4+2x-4   

                 h

 

              -2h = -2

                h

 

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