Section 1 - Functions


 

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

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 + 4x + 9

 

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; set inside ≥ 0 and solve --> domain

2. variables in denominator of fraction; set denominator = 0 and solve --> leave out of domain

 

 

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