Section 3.3
Graphs of Basic Functions; Piecewise Functions
Objective 1:
Sketching the Graphs of the Basic Functions
We begin by discussing the graphs of two specific linear functions.
Recall that a linear function has the
form
( )
f x
mx
b
=
+
where
m
is the slope of the line and
b
represents the
y
coordinate of the
y
intercept.
We start our discussion of the basic functions by looking at the
constant function
, that is, the linear
function with
0
m
=
, the graph of which is a horizontal line.
1.
The Constant Function
=
( )
f x
b
Notice that there are no arrows used at either end of the graph representing the constant function above.
From this point forward in the text, unless the graph contains a definitive endpoint (shown by either an
open dot or a closed dot) then it will be understood that the graph extends indefinitely in the same
direction.
The
identity function
defined by
( )
f x
x
=
is another linear function with
1
m
=
and
0.
b
=
It assigns to
each number in the domain the exact same number in the range.
2.
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 Spring '09
 moshe
 Algebra, Continuous function, Complex number, absolute value function

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