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Sec. 2.1 –
Graphs of Basic Functions and Relations; Symmetry
Continuity of functions
A function is said to be
continuous
if you can draw its graph from its leftmost domain
value to its rightmost domain value without lifting your pencil up off of the paper.
An entire function may not be continuous, but it can be continuous over an interval of its
domain.
See examples P. 90.
Increasing functions : as
x increases from left to right, y increases (graph goes
up).
Ex. y = 3x –1
Decreasing functions : as x increases from left to right, y decreases (graph goes down)
Ex. y = 2x + 3
Constant functions : as x increases from left to right, y stays the same (graph is
horizontal)
ex. y = 3
For the intervals over which the function is increasing, decreasing, or being constant, we
refer to the
xvalues
that cause y to increase, decrease, or be constant.
We generally want to specify the intervals over which the function is increasing,
decreasing, or remaining constant.
Use
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This note was uploaded on 06/13/2011 for the course MTH 141 taught by Professor Lebre during the Fall '06 term at Moraine Valley Community College.
 Fall '06
 Lebre
 Algebra, Continuity

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