How do you graph y=(0.5)x and state the domain and range?
Answers
graph{(0.5)^x [-10, 10, -5, 5]}
domain:
(
−
∞
,
∞
)
range:
(
0
,
∞
)
Explanation:
y
=
(
0.5
)
x
domain (the values that
x
could take):
x
could be substituted for all real numbers, including
π
and
e
.
this means that the values that
x
could take go from
−
∞
to
∞
.
∴
−
∞
and
∞
are the domain, and are written as
(
−
∞
,
∞
)
range (the values that
y
could take):
y
=
(
0.5
)
x
the roots (square, cube, etc.) of negative numbers are lateral (
i
or a factor/multiple of this), and 0.5 is a real number-
∴
(
0.5
)
x
>
0
.
since the value of
(
0.5
)
x
decreases as
x
increases,
y
gradually goes towards
0
.
although it does not actually reach
0
,
0
is its limit as
x
approaches
∞
.
this means that the values
y
could take go from
0
to
∞
.
∴
0
and
∞
are the range, and are written as
(
0
,
∞
)
.