1.0 - Complete Graphs
A graph is complete if what we see in the viewing window shows all the important features of the
graph.
BUT, can we ever really be certain that there isn't some interesting behavior outside the viewing
window?
Example: y 
1 4
x  10x3  2x 2  3
2
1.1 - Functions
I. Definition: A function is a rule that assigns to each element in the domain one and only one
element in the range.
II. Notation: y  f (x) and ( x, y)  ( x, f ( x))
Recall the vertical line test:
III. Piece-wise Defined Functions (Defined in pieces - graphed in pieces)
x
 x, x  0
= 
 x, x  0
1.
f ( x) =
2.
 x, x  0
f ( x)  
 x, x0
3.
 2,  3  x  0

f ( x)  x  1, 0  x  2
 x2 , 2  x  3

IV. A little more on Domain
Example:
Example:
f ( x) 
4  3x
V. Other function terminology (informally)
A function f is said to be
- increasing on an interval (a, b) if the graph of f rises while moving left to right
- decreasing on an interval (a, b) if the graph of f falls while moving left to right
- concave up on an interval (a, b) if the graph of f bends upward
- concave down on an interval (a, b) if the graph of f bends downward
- continuous on an interval I if the graph of f does not have any breaks, gaps or holes in I
- discontinuous at c if the graph of f has a break or gap at c, f (c) or if f (c) is undefined
(in other words, the graph has a hole at x  c ).
HW 1.1 # 1 - 23 (odd), 25 - 31, 36, 40, 51, 55, 58, 59, 63, 65