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Section 1 - Functions

This version was saved 16 years, 3 months ago View current version     Page history
Saved by PBworks
on December 20, 2007 at 12:11:28 pm
 

 

Functions

 

Meg Modzelewski

Kristin Huntington

 

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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