Explanation:
Last option
−1 • f(x)
Explanation:
The function
�
(
�
)
=
(
0.5
)
�
f(x)=(0.5)
x
passes through point (-1, 2) because:
�
(
−
1
)
=
(
0.5
)
−
1
=
1
(
0.5
)
=
2
f(−1)=(0.5)
−1
=
(0.5)
1
=2
and also goes through the point (0, 1)
Because:
�
(
0
)
=
(
0.5
)
0
=
1
f(0)=(0.5)
0
=1
Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of
�
(
�
)
=
(
0.5
)
�
f(x)=(0.5)
x
reflected on the axis x. This means that if the point
(
�
0
,
�
0
)
(x
0
,y
0
) belongs to f(x), then the point
(
�
0
,
−
�
0
)
(x
0
,−y
0
) belongs to the transformed function
The transformation that reflects the graph of a function on the x-axis is.
�
=
�
�
(
�
)
y=cf(x)
Where c is a negative number. In this case
�
=
−
1
c=−1
Then the transformation is:
�
=
−
1
∗
�
(
�
)
y=−1∗f(x)
and the transformed function is:
�
(
�
)
=
−
(
0.5
)
�
f(x)=−(0.5)
x