sketch the graph and find the domain and range of function f(x)=[X]
Answers
Answer:
The domain of
f
(
x
)
=
x
is the whole of the real numbers
R
. The range is also the whole of
R
.
Explanation:
Given:
f
(
x
)
=
x
The domain of
f
(
x
)
is the set of values for which
f
(
x
)
is defined. In the context of Algebra I that means a subset of the real numbers
R
. In the case of the given
f
(
x
)
, it is well defined for any
x
∈
R
, so the domain is the whole of
R
, i.e.
(
−
∞
,
∞
)
The range of
f
(
x
)
is the set of values that it can take for some value of
x
. Given any real number
y
, let
x
=
y
. Then
f
(
x
)
=
x
=
y
. So the range of
f
(
x
)
is the whole of
R
too.
The graph of
f
(
x
)
=
x
is a diagonal line like this:
# graph{x [-10, 10, -5, 5]}
For every
x
coordinate there is a corresponding point on the line. That tells us that the domain of
f
(
x
)
is the whole of
R
.
For every
y
coordinate there is a corresponding point on the line. That tells us that the range of
f
(
x
)
is the whole of
R
.
Step-by-step explanation:
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