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Math Problems
Algebra 2
Describe function transformations
What kind of transformation converts the graph of
f
(
x
)
=
−
4
∣
x
−
2
∣
f(x) = -4|x - 2|
f
(
x
)
=
−
4∣
x
−
2∣
into the graph of
g
(
x
)
=
−
4
∣
x
−
2
∣
−
6
g(x) = -4|x - 2| - 6
g
(
x
)
=
−
4∣
x
−
2∣
−
6
?
\newline
Choices:
\newline
(A) translation
6
6
6
units down
\newline
(B) translation
6
6
6
units up
\newline
(C) translation
6
6
6
units left
\newline
(D) translation
6
6
6
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
4
∣
x
−
8
∣
+
8
f(x) = 4|x - 8| + 8
f
(
x
)
=
4∣
x
−
8∣
+
8
into the graph of
g
(
x
)
=
4
∣
x
−
8
∣
−
1
g(x) = 4|x - 8| - 1
g
(
x
)
=
4∣
x
−
8∣
−
1
?
\newline
Choices:
\newline
(A) translation
9
9
9
units down
\newline
(B) translation
9
9
9
units up
\newline
(C) translation
9
9
9
units right
\newline
(D) translation
9
9
9
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
10
∣
x
−
8
∣
+
4
f(x) = 10|x - 8| + 4
f
(
x
)
=
10∣
x
−
8∣
+
4
into the graph of
g
(
x
)
=
10
∣
x
−
8
∣
+
9
g(x) = 10|x - 8| + 9
g
(
x
)
=
10∣
x
−
8∣
+
9
?
\newline
Choices:
\newline
(A) translation
5
5
5
units left
\newline
(B) translation
5
5
5
units right
\newline
(C) translation
5
5
5
units down
\newline
(D) translation
5
5
5
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
6
∣
x
+
5
∣
+
4
f(x) = -6|x + 5| + 4
f
(
x
)
=
−
6∣
x
+
5∣
+
4
into the graph of
g
(
x
)
=
−
6
∣
x
+
5
∣
+
10
g(x) = -6|x + 5| + 10
g
(
x
)
=
−
6∣
x
+
5∣
+
10
?
\newline
Choices:
\newline
(A) translation
6
6
6
units left
\newline
(B) translation
6
6
6
units down
\newline
(C) translation
6
6
6
units right
\newline
(D) translation
6
6
6
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
2
∣
x
−
3
∣
+
7
f(x) = 2|x - 3| + 7
f
(
x
)
=
2∣
x
−
3∣
+
7
into the graph of
g
(
x
)
=
2
∣
x
+
7
∣
+
7
g(x) = 2|x + 7| + 7
g
(
x
)
=
2∣
x
+
7∣
+
7
?
\newline
Choices:
\newline
(A) translation
10
10
10
units left
\newline
(B) translation
10
10
10
units down
\newline
(C) translation
10
10
10
units right
\newline
(D) translation
10
10
10
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
4
∣
x
+
2
∣
+
8
f(x) = 4|x + 2| + 8
f
(
x
)
=
4∣
x
+
2∣
+
8
into the graph of
g
(
x
)
=
4
∣
x
+
2
∣
+
5
g(x) = 4|x + 2| + 5
g
(
x
)
=
4∣
x
+
2∣
+
5
?
\newline
Choices:
\newline
(A) translation
3
3
3
units left
\newline
(B) translation
3
3
3
units right
\newline
(C) translation
3
3
3
units down
\newline
(D) translation
3
3
3
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
3
∣
x
−
4
∣
+
5
f(x) = -3|x - 4| + 5
f
(
x
)
=
−
3∣
x
−
4∣
+
5
into the graph of
g
(
x
)
=
−
3
∣
x
−
7
∣
+
5
g(x) = -3|x - 7| + 5
g
(
x
)
=
−
3∣
x
−
7∣
+
5
?
\newline
Choices:
\newline
(A) translation
3
3
3
units right
\newline
(B) translation
3
3
3
units left
\newline
(C) translation
3
3
3
units up
\newline
(D) translation
3
3
3
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
8
∣
x
−
6
∣
+
9
f(x) = -8|x - 6| + 9
f
(
x
)
=
−
8∣
x
−
6∣
+
9
into the graph of
g
(
x
)
=
−
8
∣
x
−
2
∣
+
9
g(x) = -8|x - 2| + 9
g
(
x
)
=
−
8∣
x
−
2∣
+
9
?
\newline
Choices:
\newline
(A) translation
4
4
4
units up
\newline
(B) translation
4
4
4
units right
\newline
(C) translation
4
4
4
units left
\newline
(D) translation
4
4
4
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
4
(
x
−
5
)
2
+
10
f(x) = 4(x - 5)^2 + 10
f
(
x
)
=
4
(
x
−
5
)
2
+
10
into the graph of
g
(
x
)
=
4
(
x
−
5
)
2
+
4
g(x) = 4(x - 5)^2 + 4
g
(
x
)
=
4
(
x
−
5
)
2
+
4
?
\newline
Choices:
\newline
(A) translation
6
6
6
units down
\newline
(B) translation
6
6
6
units left
\newline
(C) translation
6
6
6
units up
\newline
(D) translation
6
6
6
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
3
∣
x
−
3
∣
−
9
f(x) = 3|x - 3| - 9
f
(
x
)
=
3∣
x
−
3∣
−
9
into the graph of
g
(
x
)
=
3
∣
x
+
2
∣
−
9
g(x) = 3|x + 2| - 9
g
(
x
)
=
3∣
x
+
2∣
−
9
?
\newline
Choices:
\newline
(A) translation
5
5
5
units left
\newline
(B) translation
5
5
5
units up
\newline
(C) translation
5
5
5
units down
\newline
(D) translation
5
5
5
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
3
∣
x
+
4
∣
f(x) = 3|x + 4|
f
(
x
)
=
3∣
x
+
4∣
into the graph of
g
(
x
)
=
3
∣
x
+
4
∣
−
5
g(x) = 3|x + 4| - 5
g
(
x
)
=
3∣
x
+
4∣
−
5
?
\newline
Choices:
\newline
(A) translation
5
5
5
units down
\newline
(B) translation
5
5
5
units up
\newline
(C) translation
5
5
5
units right
\newline
(D) translation
5
5
5
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
7
∣
x
−
4
∣
−
2
f(x) = 7|x - 4| - 2
f
(
x
)
=
7∣
x
−
4∣
−
2
into the graph of
g
(
x
)
=
7
∣
x
+
2
∣
−
2
g(x) = 7|x + 2| - 2
g
(
x
)
=
7∣
x
+
2∣
−
2
?
\newline
Choices:
\newline
(A) translation
6
6
6
units right
\newline
(B) translation
6
6
6
units down
\newline
(C) translation
6
6
6
units up
\newline
(D) translation
6
6
6
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
9
∣
x
−
2
∣
−
2
f(x) = 9|x - 2| - 2
f
(
x
)
=
9∣
x
−
2∣
−
2
into the graph of
g
(
x
)
=
9
∣
x
+
1
∣
−
2
g(x) = 9|x + 1| - 2
g
(
x
)
=
9∣
x
+
1∣
−
2
?
\newline
Choices:
\newline
(A) translation
3
3
3
units left
\newline
(B) translation
3
3
3
units up
\newline
(C) translation
3
3
3
units right
\newline
(D) translation
3
3
3
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
8
∣
x
+
4
∣
−
3
f(x) = -8|x + 4| - 3
f
(
x
)
=
−
8∣
x
+
4∣
−
3
into the graph of
g
(
x
)
=
−
8
∣
x
−
6
∣
−
3
g(x) = -8|x - 6| - 3
g
(
x
)
=
−
8∣
x
−
6∣
−
3
?
\newline
Choices:
\newline
(A) translation
10
10
10
units right
\newline
(B) translation
10
10
10
units left
\newline
(C) translation
10
10
10
units up
\newline
(D) translation
10
10
10
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
3
∣
x
+
8
∣
−
2
f(x) = -3|x + 8| - 2
f
(
x
)
=
−
3∣
x
+
8∣
−
2
into the graph of
g
(
x
)
=
−
3
∣
x
+
8
∣
g(x) = -3|x + 8|
g
(
x
)
=
−
3∣
x
+
8∣
?
\newline
Choices:
\newline
(A) translation
2
2
2
units up
\newline
(B) translation
2
2
2
units right
\newline
(C) translation
2
2
2
units down
\newline
(D) translation
2
2
2
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
2
∣
x
−
4
∣
−
2
f(x) = -2|x - 4| - 2
f
(
x
)
=
−
2∣
x
−
4∣
−
2
into the graph of
g
(
x
)
=
−
2
∣
x
−
4
∣
−
6
g(x) = -2|x - 4| - 6
g
(
x
)
=
−
2∣
x
−
4∣
−
6
?
\newline
Choices:
\newline
(A) translation
4
4
4
units right
\newline
(B) translation
4
4
4
units up
\newline
(C) translation
4
4
4
units left
\newline
(D) translation
4
4
4
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
8
∣
x
−
5
∣
+
5
f(x) = 8|x - 5| + 5
f
(
x
)
=
8∣
x
−
5∣
+
5
into the graph of
g
(
x
)
=
8
∣
x
−
5
∣
+
10
g(x) = 8|x - 5| + 10
g
(
x
)
=
8∣
x
−
5∣
+
10
?
\newline
Choices:
\newline
(A) translation
5
5
5
units up
\newline
(B) translation
5
5
5
units left
\newline
(C) translation
5
5
5
units down
\newline
(D) translation
5
5
5
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
6
∣
x
−
4
∣
+
1
f(x) = -6|x - 4| + 1
f
(
x
)
=
−
6∣
x
−
4∣
+
1
into the graph of
g
(
x
)
=
−
6
∣
x
−
4
∣
+
8
g(x) = -6|x - 4| + 8
g
(
x
)
=
−
6∣
x
−
4∣
+
8
?
\newline
Choices:
\newline
(A) translation
7
7
7
units left
\newline
(B) translation
7
7
7
units down
\newline
(C) translation
7
7
7
units up
\newline
(D) translation
7
7
7
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
8
∣
x
−
2
∣
−
2
f(x) = 8|x - 2| - 2
f
(
x
)
=
8∣
x
−
2∣
−
2
into the graph of
g
(
x
)
=
8
∣
x
+
4
∣
−
2
g(x) = 8|x + 4| - 2
g
(
x
)
=
8∣
x
+
4∣
−
2
?
\newline
Choices:
\newline
(A) translation
6
6
6
units right
\newline
(B) translation
6
6
6
units up
\newline
(C) translation
6
6
6
units left
\newline
(D) translation
6
6
6
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
7
∣
x
−
6
∣
f(x) = 7|x - 6|
f
(
x
)
=
7∣
x
−
6∣
into the graph of
g
(
x
)
=
7
∣
x
∣
g(x) = 7|x|
g
(
x
)
=
7∣
x
∣
?
\newline
Choices:
\newline
(A) translation
6
6
6
units right
\newline
(B) translation
6
6
6
units down
\newline
(C) translation
6
6
6
units up
\newline
(D) translation
6
6
6
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
4
∣
x
+
1
∣
−
3
f(x) = 4|x + 1| - 3
f
(
x
)
=
4∣
x
+
1∣
−
3
into the graph of
g
(
x
)
=
4
∣
x
+
9
∣
−
3
g(x) = 4|x + 9| - 3
g
(
x
)
=
4∣
x
+
9∣
−
3
?
\newline
Choices:
\newline
(A) translation
8
8
8
units down
\newline
(B) translation
8
8
8
units up
\newline
(C) translation
8
8
8
units left
\newline
(D) translation
8
8
8
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
6
∣
x
+
1
∣
+
8
f(x) = 6|x + 1| + 8
f
(
x
)
=
6∣
x
+
1∣
+
8
into the graph of
g
(
x
)
=
6
∣
x
+
1
∣
−
1
g(x) = 6|x + 1| - 1
g
(
x
)
=
6∣
x
+
1∣
−
1
?
\newline
Choices:
\newline
(A) translation
9
9
9
units left
\newline
(B) translation
9
9
9
units up
\newline
(C) translation
9
9
9
units right
\newline
(D) translation
9
9
9
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
7
∣
x
−
2
∣
−
10
f(x) = 7|x - 2| - 10
f
(
x
)
=
7∣
x
−
2∣
−
10
into the graph of
g
(
x
)
=
7
∣
x
+
3
∣
−
10
g(x) = 7|x + 3| - 10
g
(
x
)
=
7∣
x
+
3∣
−
10
?
\newline
Choices:
\newline
(A) translation
5
5
5
units left
\newline
(B) translation
5
5
5
units up
\newline
(C) translation
5
5
5
units right
\newline
(D) translation
5
5
5
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
5
∣
x
−
1
∣
f(x) = 5|x - 1|
f
(
x
)
=
5∣
x
−
1∣
into the graph of
g
(
x
)
=
5
∣
x
−
1
∣
−
10
g(x) = 5|x - 1| - 10
g
(
x
)
=
5∣
x
−
1∣
−
10
?
\newline
Choices:
\newline
(A) translation
10
10
10
units up
\newline
(B) translation
10
10
10
units down
\newline
(C) translation
10
10
10
units left
\newline
(D) translation
10
10
10
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
6
∣
x
+
9
∣
+
5
f(x) = 6|x + 9| + 5
f
(
x
)
=
6∣
x
+
9∣
+
5
into the graph of
g
(
x
)
=
6
∣
x
+
9
∣
+
1
g(x) = 6|x + 9| + 1
g
(
x
)
=
6∣
x
+
9∣
+
1
?
\newline
Choices:
\newline
(A) translation
4
4
4
units down
\newline
(B) translation
4
4
4
units up
\newline
(C) translation
4
4
4
units left
\newline
(D) translation
4
4
4
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
6
∣
x
−
7
∣
−
2
f(x) = 6|x - 7| - 2
f
(
x
)
=
6∣
x
−
7∣
−
2
into the graph of
g
(
x
)
=
6
∣
x
−
7
∣
+
1
g(x) = 6|x - 7| + 1
g
(
x
)
=
6∣
x
−
7∣
+
1
?
\newline
Choices:
\newline
(A) translation
3
3
3
units left
\newline
(B) translation
3
3
3
units right
\newline
(C) translation
3
3
3
units up
\newline
(D) translation
3
3
3
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
5
(
x
−
2
)
2
+
4
f(x) = 5(x - 2)^2 + 4
f
(
x
)
=
5
(
x
−
2
)
2
+
4
into the graph of
g
(
x
)
=
5
(
x
+
5
)
2
+
4
g(x) = 5(x + 5)^2 + 4
g
(
x
)
=
5
(
x
+
5
)
2
+
4
?
\newline
Choices:
\newline
(A) translation
7
7
7
units down
\newline
(B) translation
7
7
7
units up
\newline
(C) translation
7
7
7
units left
\newline
(D) translation
7
7
7
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
3
∣
x
+
7
∣
−
4
f(x) = 3|x + 7| - 4
f
(
x
)
=
3∣
x
+
7∣
−
4
into the graph of
g
(
x
)
=
3
∣
x
+
7
∣
+
6
g(x) = 3|x + 7| + 6
g
(
x
)
=
3∣
x
+
7∣
+
6
?
\newline
Choices:
\newline
(A) translation
10
10
10
units right
\newline
(B) translation
10
10
10
units left
\newline
(C) translation
10
10
10
units down
\newline
(D) translation
10
10
10
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
3
∣
x
+
10
∣
−
8
f(x) = -3|x + 10| - 8
f
(
x
)
=
−
3∣
x
+
10∣
−
8
into the graph of
g
(
x
)
=
−
3
∣
x
+
10
∣
−
9
g(x) = -3|x + 10| - 9
g
(
x
)
=
−
3∣
x
+
10∣
−
9
?
\newline
Choices:
\newline
(A) translation
1
1
1
unit right
\newline
(B) translation
1
1
1
unit down
\newline
(C) translation
1
1
1
unit left
\newline
(D) translation
1
1
1
unit up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
7
∣
x
+
4
∣
+
7
f(x) = -7|x + 4| + 7
f
(
x
)
=
−
7∣
x
+
4∣
+
7
into the graph of
g
(
x
)
=
−
7
∣
x
−
3
∣
+
7
g(x) = -7|x - 3| + 7
g
(
x
)
=
−
7∣
x
−
3∣
+
7
?
\newline
Choices:
\newline
(A) translation
7
7
7
units down
\newline
(B) translation
7
7
7
units right
\newline
(C) translation
7
7
7
units left
\newline
(D) translation
7
7
7
units up
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
9
∣
x
+
6
∣
−
4
f(x) = 9|x + 6| - 4
f
(
x
)
=
9∣
x
+
6∣
−
4
into the graph of
g
(
x
)
=
9
∣
x
+
6
∣
−
9
g(x) = 9|x + 6| - 9
g
(
x
)
=
9∣
x
+
6∣
−
9
?
\newline
Choices:
\newline
(A) translation
5
5
5
units up
\newline
(B) translation
5
5
5
units left
\newline
(C) translation
5
5
5
units down
\newline
(D) translation
5
5
5
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
2
∣
x
−
5
∣
+
1
f(x) = 2|x - 5| + 1
f
(
x
)
=
2∣
x
−
5∣
+
1
into the graph of
g
(
x
)
=
2
∣
x
+
5
∣
+
1
g(x) = 2|x + 5| + 1
g
(
x
)
=
2∣
x
+
5∣
+
1
?
\newline
Choices:
\newline
(A) translation
10
10
10
units down
\newline
(B) translation
10
10
10
units up
\newline
(C) translation
10
10
10
units left
\newline
(D) translation
10
10
10
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
4
∣
x
−
7
∣
+
3
f(x) = -4|x - 7| + 3
f
(
x
)
=
−
4∣
x
−
7∣
+
3
into the graph of
g
(
x
)
=
−
4
∣
x
−
7
∣
−
1
g(x) = -4|x - 7| - 1
g
(
x
)
=
−
4∣
x
−
7∣
−
1
?
\newline
Choices:
\newline
(A) translation
4
4
4
units left
\newline
(B) translation
4
4
4
units up
\newline
(C) translation
4
4
4
units right
\newline
(D) translation
4
4
4
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
∣
x
−
4
∣
−
3
f(x) = |x - 4| - 3
f
(
x
)
=
∣
x
−
4∣
−
3
into the graph of
g
(
x
)
=
∣
x
+
2
∣
−
3
g(x) = |x + 2| - 3
g
(
x
)
=
∣
x
+
2∣
−
3
?
\newline
Choices:
\newline
(A) translation
6
6
6
units up
\newline
(B) translation
6
6
6
units right
\newline
(C) translation
6
6
6
units left
\newline
(D) translation
6
6
6
units down
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
10
∣
x
∣
+
3
f(x) = -10|x| + 3
f
(
x
)
=
−
10∣
x
∣
+
3
into the graph of
g
(
x
)
=
−
10
∣
x
−
6
∣
+
3
g(x) = -10|x - 6| + 3
g
(
x
)
=
−
10∣
x
−
6∣
+
3
?
\newline
Choices:
\newline
(A) translation
6
6
6
units right
\newline
(B) translation
6
6
6
units down
\newline
(C) translation
6
6
6
units up
\newline
(D) translation
6
6
6
units left
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
5
∣
x
+
10
∣
−
6
f(x) = 5|x + 10| - 6
f
(
x
)
=
5∣
x
+
10∣
−
6
into the graph of
g
(
x
)
=
5
∣
x
+
5
∣
−
6
g(x) = 5|x + 5| - 6
g
(
x
)
=
5∣
x
+
5∣
−
6
?
\newline
Choices:
\newline
(A) translation
5
5
5
units down
\newline
(B) translation
5
5
5
units up
\newline
(C) translation
5
5
5
units left
\newline
(D) translation
5
5
5
units right
Get tutor help
What kind of transformation converts the graph of
f
(
x
)
=
−
3
x
2
−
4
f(x) = -3x^2 - 4
f
(
x
)
=
−
3
x
2
−
4
into the graph of
g
(
x
)
=
−
3
x
2
+
6
g(x) = -3x^2 + 6
g
(
x
)
=
−
3
x
2
+
6
?
\newline
Choices:
\newline
[A]translation 10 units up
\text{[A]translation 10 units up}
[A]translation 10 units up
\newline
[B]translation 10 units down
\text{[B]translation 10 units down}
[B]translation 10 units down
\newline
[C]translation 10 units left
\text{[C]translation 10 units left}
[C]translation 10 units left
\newline
[D]translation 10 units right
\text{[D]translation 10 units right}
[D]translation 10 units right
Get tutor help
