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Math Problems
Precalculus
Function transformation rules
ind rational ranced
\newline
□
\square
□
exponents: ...
\newline
y
1
2
⋅
16
x
2
y
3
2
+
8
y
2
3
y^{\frac{1}{2}} \cdot \sqrt[3]{16 x^{2} y^{\frac{3}{2}}+8 y^{2}}
y
2
1
⋅
3
16
x
2
y
2
3
+
8
y
2
\newline
Which of the following expressions is equivalent to the given expression assuming
y
≥
0
y \geq 0
y
≥
0
?
\newline
A)
2
y
2
x
2
+
y
1
2
3
2 y \sqrt[3]{2 x^{2}+y^{\frac{1}{2}}}
2
y
3
2
x
2
+
y
2
1
\newline
B) INCORRECT
\newline
C) INCORRECT
\newline
D) \longdiv { 7 }
\newline
E)
1
1
1
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In a pasture are horses and chickens if there are a total of
28
28
28
animals and
80
80
80
legs: how many chickens and horses?
\newline
12
12
12
horses,
16
16
16
chickens
\newline
16
16
16
horses,
12
12
12
chickens
\newline
18
18
18
horses,
10
10
10
chickens
\newline
10
10
10
horses,
18
18
18
chickens
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f
(
x
)
=
3
−
2
(
x
+
1
)
f(x)=3^{-2(x+1)}
f
(
x
)
=
3
−
2
(
x
+
1
)
\newline
Which of the following equivalent forms of the given function
f
f
f
displays, as the base or the coefficient, the
y
y
y
-coordinate of the
y
y
y
-intercept of the graph of
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
in the
x
y
x y
x
y
-plane?
\newline
A)
f
(
x
)
=
(
1
3
)
(
2
x
+
2
)
f(x)=\left(\frac{1}{3}\right)^{(2 x+2)}
f
(
x
)
=
(
3
1
)
(
2
x
+
2
)
\newline
B)
f
(
x
)
=
1
9
(
1
3
)
2
x
f(x)=\frac{1}{9}\left(\frac{1}{3}\right)^{2 x}
f
(
x
)
=
9
1
(
3
1
)
2
x
\newline
C)
f
(
x
)
=
8
1
(
−
1
2
x
−
1
2
)
f(x)=81^{\left(-\frac{1}{2} x-\frac{1}{2}\right)}
f
(
x
)
=
8
1
(
−
2
1
x
−
2
1
)
\newline
D)
f
(
x
)
=
3
(
−
2
x
−
2
)
f(x)=3^{(-2 x-2)}
f
(
x
)
=
3
(
−
2
x
−
2
)
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For
x
x
x
such that
0
<
x
<
π
2
0<x<\frac{\pi}{2}
0
<
x
<
2
π
, the expression
1
−
cos
2
x
sin
x
+
1
−
sin
2
x
cos
x
\frac{\sqrt{1-\cos ^{2} x}}{\sin x}+\frac{\sqrt{1-\sin ^{2} x}}{\cos x}
s
i
n
x
1
−
c
o
s
2
x
+
c
o
s
x
1
−
s
i
n
2
x
is equivalent to:
\newline
F.
0
0
0
\newline
G.
1
1
1
\newline
H.
2
2
2
\newline
J.
−
tan
x
-\tan x
−
tan
x
\newline
K.
sin
2
x
\sin 2 x
sin
2
x
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Simplify:
\newline
2
(
1
+
3
i
)
−
(
2
−
4
i
)
+
(
5
−
2
i
)
2(1+3 i)-(2-4 i)+(5-2 i)
2
(
1
+
3
i
)
−
(
2
−
4
i
)
+
(
5
−
2
i
)
\newline
(A)
5
+
4
i
5+4 i
5
+
4
i
\newline
(B)
13
13
13
\newline
(C)
9
+
6
i
9+6 i
9
+
6
i
\newline
(D)
5
+
8
i
5+8 i
5
+
8
i
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
7
,
7
,
7
7
,
…
\sqrt{7}, \quad 7, \quad 7 \sqrt{7}, \ldots
7
,
7
,
7
7
,
…
\newline
7
7
\frac{\sqrt{7}}{7}
7
7
\newline
7
\sqrt{7}
7
\newline
2
7
7
\frac{2 \sqrt{7}}{7}
7
2
7
\newline
2
7
2 \sqrt{7}
2
7
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
7
,
7
,
7
7
,
…
\sqrt{7}, \quad 7, \quad 7 \sqrt{7}, \quad \ldots
7
,
7
,
7
7
,
…
\newline
7
7
\frac{\sqrt{7}}{7}
7
7
\newline
7
\sqrt{7}
7
\newline
2
7
7
\frac{2 \sqrt{7}}{7}
7
2
7
\newline
2
7
2 \sqrt{7}
2
7
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Which expression has the same value as
8
y
+
(
−
2
x
)
8 y+(-2 x)
8
y
+
(
−
2
x
)
?
\newline
2
x
+
8
y
2 x+8 y
2
x
+
8
y
\newline
8
y
+
2
x
8 y+2 x
8
y
+
2
x
\newline
8
y
−
(
−
2
x
)
8 y-(-2 x)
8
y
−
(
−
2
x
)
\newline
−
2
x
−
(
−
8
y
)
-2 x-(-8 y)
−
2
x
−
(
−
8
y
)
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Determine whether the function
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
6
x=6
x
=
6
.
\newline
f
(
x
)
=
{
16
−
x
2
,
x
<
6
−
2
−
3
x
,
x
≥
6
f(x)=\left\{\begin{array}{ll} 16-x^{2}, & x<6 \\ -2-3 x, & x \geq 6 \end{array}\right.
f
(
x
)
=
{
16
−
x
2
,
−
2
−
3
x
,
x
<
6
x
≥
6
\newline
f
(
x
)
f(x)
f
(
x
)
is discontinuous at
x
=
6
x=6
x
=
6
\newline
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
6
x=6
x
=
6
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