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 =
y = ±
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) = - + 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)= 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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