Function Transformations
The graphs below show the functions
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
and
g
(
x
)
\displaystyle {g{{\left({x}\right)}}}
g
(
x
)
where:
g
(
x
)
=
a
f
(
x
)
\displaystyle {g{{\left({x}\right)}}}={a}{f{{\left({x}\right)}}}
g
(
x
)
=
a
f
(
x
)
Identify the value of '
a
'
for this transformation:
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
1
2
3
4
-1
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
[Graphs generated by this script: setBorder(5);initPicture(-1,4,-6,6);axes(1,1,1,1,1);line([1,2],[2,-1]);line([2,-1],[3,-2]);]
g
(
x
)
\displaystyle {g{{\left({x}\right)}}}
g
(
x
)
1
2
3
4
-1
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
[Graphs generated by this script: setBorder(5);initPicture(-1,4,-6,6);axes(1,1,1,1,1);line([1,-6],[2,3]);line([2,3],[3,6]);]
g
(
x
)
=
a
f
(
x
)
\displaystyle {g{{\left({x}\right)}}}={a}{f{{\left({x}\right)}}}
g
(
x
)
=
a
f
(
x
)
when
a
=
\displaystyle {a}=
a
=
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