Download notes

FUNCTIONS
RELATION:
a set of ordered pairs
EX 1:
 0,0, 1,1, 2, 4, 3,9
EX 2:
2,3, 2,7 ,  1, 4
DOMAIN: the set of all x-coordinates
RANGE: the set of all y-coordinates
FUNCTION: a relation in which each domain element corresponds to one and only one range
element.
*For every x, there is only 1 y.
WAYS OF REPRESENTING
2,3, 2,7 ,  1, 4
 0,0,1,1,2,4 ,3,9
ORDERED PAIRS
TABLE
x
0
1
2
3
y
0
1
4
9
x
2
2
-1
y
3
7
4
GRAPH
MAPPING DIAGRAM
0
1
2
3
0
1
4
9
2
-1
3
7
4
VERTICAL LINE TEST (VLT)
If every vertical line intersects a given graph at no more than one point, then the graph
represents a function.
FUNCTION NOTATION
f  x   4x  1
y  4x  1
y  f x 
f  x   "f is a function of x "
x , y   x ,f x 
EXAMPLE 1
Given y  4x  1 , evaluate f 5 , f  0  , f  7  .
EXAMPLE 2
Find, f  4  .
Find, f  1  .
State the domain and the range.
State any intercepts.
Find any symmetry that exists with respect to the
x-axis, y-axis, and/or origin.
Example 3
Find f  4  .
Find f  1  .
State the domain and the range.
State any intercepts.
Find any symmetry that exists with respect to the
x-axis, y-axis, and/or origin.
Finding the Domain of a Function
(1) For a polynomial, the domain is all real numbers.
EX:
(2)
5x3  2x2  6x  8 domain is all real numbers
For expressions that contain radicals with even indices, the radicand must be greater
than or equal to zero.
2x  3
EX:
(3)
3
domain is  ,  
2 
For fractional expressions, the denominator cannot be equal to zero.
x
EX:
domain is  ,1   1,  
x 1
Examples
State the domain for each of the following functions.
EX 1: g  x   x3  1
EX 2: h  x   3x  4
EX 3: p  x   4x
2x  1
EX 4: q  x   x2  8x  12
EX 5: m  x  
Function or Not a Function
Graphically – VLT
By Equation –
1. Try to solve for y in terms of x.
2. Decide whether each value of x corresponds to exactly one value of y.
Example:
Which of the equations represent(s) y as a function of x?
a. x2  y  1
b.
x  y2  1
7
x  16
2