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Math Problems
Precalculus
Even and odd functions
\newline
If
∣
a
⃗
+
b
⃗
∣
=
∣
a
⃗
−
b
⃗
∣
|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|
∣
a
+
b
∣
=
∣
a
−
b
∣
prove that
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
are perpendicular
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For the rotation
−
29
3
∘
-293^{\circ}
−
29
3
∘
, find the coterminal angle from
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, the quadrant, and the reference angle.
\newline
The coterminal angle is
□
∘
\square^{\circ}
□
∘
, which lies in Quadrant
□
\square
□
, with a reference angle of
□
∘
\square^{\circ}
□
∘
.
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Express as a complex number in simplest a+bi form:
\newline
10
−
5
i
−
5
−
6
i
\frac{10-5 i}{-5-6 i}
−
5
−
6
i
10
−
5
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
4
−
3
i
−
4
−
4
i
\frac{4-3 i}{-4-4 i}
−
4
−
4
i
4
−
3
i
\newline
Answer:
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Determine if the lines are parallel, perpendicular, or neither.
\newline
a)
\newline
b)
\newline
\begin{align*}y&=-2x+3\-3y&=6x+15\end{align*}
\newline
c)
\newline
\begin{align*}3x+4y&=4\4x+3y&=-21\end{align*}
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Suppose that the functions
\newline
f
f
f
and
\newline
g
g
g
are defined as follows.
\newline
f
(
x
)
=
8
x
f(x)=\frac{8}{x}
f
(
x
)
=
x
8
\quad
g
(
x
)
=
3
x
+
9
g(x)=\frac{3}{x+9}
g
(
x
)
=
x
+
9
3
\newline
Find
\newline
g
f
\frac{g}{f}
f
g
. Then, give its domain using an interval or union of intervals. Simplify your answers.
\newline
(
g
f
)
(
x
)
=
[
\left(\frac{g}{f}\right)(x)=\left[\right.
(
f
g
)
(
x
)
=
[
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or each equation, determine whether its graph is symmetric with respect to the
x
x
x
-axis, the
y
y
y
-axis, and the heck all symmetries that apply.
\newline
(a)
x
2
+
y
+
2
=
0
x^{2}+y+2=0
x
2
+
y
+
2
=
0
\newline
(b)
y
=
5
x
3
+
2
y=5 x^{3}+2
y
=
5
x
3
+
2
\newline
Symmetry:
\newline
Symmetry:
\newline
x
x
x
-axis
\newline
x
x
x
-axis
\newline
y
y
y
-axis
\newline
y
y
y
-axis
\newline
origin
\newline
origin
\newline
none of the above
\newline
none of the above
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Determine whether the function
f
(
x
)
=
−
7
x
4
−
6
x
2
+
2
x
6
f(x)=-7 x^{4}-6 x^{2}+2 x^{6}
f
(
x
)
=
−
7
x
4
−
6
x
2
+
2
x
6
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
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