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Math Problems
Algebra 1
Transformations of absolute value functions: translations, reflections, and dilations
Graph
g
(
x
)
=
5
∣
x
−
6
∣
+
2
g(x)=5|x-6|+2
g
(
x
)
=
5∣
x
−
6∣
+
2
.
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Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
∣
x
∣
−
10
y=|x|-10
y
=
∣
x
∣
−
10
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
∣
x
∣
−
6
y=|x|-6
y
=
∣
x
∣
−
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
4
-4
−
4
.
\newline
y
=
∣
x
∣
−
5
y=|x|-5
y
=
∣
x
∣
−
5
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
∣
x
∣
−
6
y=|x|-6
y
=
∣
x
∣
−
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
8
-8
−
8
.
\newline
y
=
∣
x
∣
−
6
y=|x|-6
y
=
∣
x
∣
−
6
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
9
-9
−
9
.
\newline
y
=
∣
x
∣
−
4
y=|x|-4
y
=
∣
x
∣
−
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
1
-1
−
1
.
\newline
y
=
∣
x
∣
−
12
y=|x|-12
y
=
∣
x
∣
−
12
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
12
-12
−
12
.
\newline
y
=
∣
x
∣
+
4
y=|x|+4
y
=
∣
x
∣
+
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
7
7
7
.
\newline
y
=
∣
x
∣
−
10
y=|x|-10
y
=
∣
x
∣
−
10
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
11
-11
−
11
.
\newline
y
=
∣
x
∣
−
1
y=|x|-1
y
=
∣
x
∣
−
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
∣
x
∣
−
1
y=|x|-1
y
=
∣
x
∣
−
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
10
-10
−
10
.
\newline
y
=
∣
x
∣
−
4
y=|x|-4
y
=
∣
x
∣
−
4
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
9
-9
−
9
.
\newline
y
=
∣
x
∣
+
10
y=|x|+10
y
=
∣
x
∣
+
10
\newline
Answer:
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f
(
x
)
=
(
x
−
10
)
2
−
49
f(x)=(x-10)^{2}-49
f
(
x
)
=
(
x
−
10
)
2
−
49
\newline
At what values of
x
x
x
does the graph of the function intersect the
x
x
x
-axis?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
17
,
x
=
3
x=17, x=3
x
=
17
,
x
=
3
\newline
(B)
x
=
17
,
x
=
−
3
x=17, x=-3
x
=
17
,
x
=
−
3
\newline
(C)
x
=
−
17
,
x
=
3
x=-17, x=3
x
=
−
17
,
x
=
3
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
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The graph of
y
=
∣
x
∣
y=|x|
y
=
∣
x
∣
is shifted down by
9
9
9
units.
\newline
What is the equation of the new graph?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
∣
x
∣
−
9
y=|x|-9
y
=
∣
x
∣
−
9
\newline
(B)
y
=
∣
x
+
9
∣
y=|x+9|
y
=
∣
x
+
9∣
\newline
(C)
y
=
∣
x
∣
+
9
y=|x|+9
y
=
∣
x
∣
+
9
\newline
(D)
y
=
∣
x
−
9
∣
y=|x-9|
y
=
∣
x
−
9∣
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Find
g
(
x
)
g(x)
g
(
x
)
, where
g
(
x
)
g(x)
g
(
x
)
is the translation
2
2
2
units left of
f
(
x
)
=
∣
x
∣
f(x) = |x|
f
(
x
)
=
∣
x
∣
.
\newline
Write your answer in the form
a
∣
x
−
h
∣
+
k
a|x - h| + k
a
∣
x
−
h
∣
+
k
, where
a
a
a
,
h
h
h
, and
k
k
k
are integers.
\newline
g
(
x
)
=
g(x) =
g
(
x
)
=
______
\newline
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