Catalogue of Important Functions
We list several important functions, draw their graphs and indicate domains and ranges.
In the forthcoming sections we will study their properties and use them in various
applications. As well, we will add more functions to our catalogue.
(1) The function
f
(
x
)
=
c
where
c
is a real number is a
constant function
. It assigns the
same number
c
to all values of the independent variable
x
. Its domain is the set of real
numbers, and the range consists of the single value
c
. The graph in Figure 1.2.D shows
the constant function
f
(
x
)
=
2
.
x
y
O
f
(
x
)
=
2
2
Figure 1.2.D
Constant function
(2) The function
f
(
x
)
=
mx
+
b
, where
m
and
b
are real numbers, is called a
linear
function
. Its graph is a line of slope
m
and
y
intercept
b
. When
m
≠
0
, then both
domain and range consist of all real numbers. If
m
=
0
, the line is horizontal, so it
represents a constant function
f
(
x
)
=
b
. The special case
y
=
x
is a line of slope
1
through the origin, see Figure 1.2.E. Sometimes we calculate the linear function from the
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 Spring '10
 kuzak
 Derivative, Quadratic equation, Continuous function, Complex number

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