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.) x^{2}+ y= 1
y= -x^{2} +1
Yes it is a function because it passes the vertical line test.
b.) -x+Y^{2} =1
Y^{2} = x+1
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)= -x^{2}+4x+1 find: f(2), h(x+1)
f(2)= -2^{2}+4(2)+1
= -4+8+1
= 5
h(x+2) = - + 4(x+2) +1
= -(x^{2 }+ 4x + 4) + 4x + 8 + 1
= -x^{2 }- 4x - 4x + 4x + 8 + 1
= -x^{2 }+ 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)= D:[0,∞)
f(x)= 1/(x^{2}-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
Comments (1)
Anonymous said
at 8:17 pm on Jan 8, 2008
One of your examples doesn't have correct work... and check your spacing on the fractions. But otherwise, nice job! 18/20
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