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Math Problems
Algebra 1
Domain and range of quadratic functions: equations
What does the set
{
x
∣
x
≥
−
15
}
\{x | x \geq -15\}
{
x
∣
x
≥
−
15
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than
−
15
-15
−
15
\newline
(B)all numbers greater than or equal to
−
15
-15
−
15
\newline
(C)all numbers equal to
−
15
-15
−
15
\newline
(D)all numbers less than
−
15
-15
−
15
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What does the set
{
x
∣
x
≤
10
}
\{x | x \leq 10\}
{
x
∣
x
≤
10
}
represent?
\newline
Choices:
\newline
(A)all numbers less than
10
10
10
\newline
(B)all numbers less than or equal to
10
10
10
\newline
(C)all numbers greater than
10
10
10
\newline
(D)all numbers greater than or equal to
10
10
10
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What does the set
{
x
∣
x
≥
−
15
}
\{x | x \geq -15\}
{
x
∣
x
≥
−
15
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than
−
15
-15
−
15
\newline
(B)all numbers less than
−
15
-15
−
15
\newline
(C)all numbers equal to
−
15
-15
−
15
\newline
(D)all numbers greater than or equal to
−
15
-15
−
15
Get tutor help
What does the set
{
x
∣
x
≤
10
}
\{x | x \leq 10\}
{
x
∣
x
≤
10
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than
10
10
10
\newline
(B)all numbers greater than or equal to
10
10
10
\newline
(C)all numbers less than
10
10
10
\newline
(D)all numbers less than or equal to
10
10
10
Get tutor help
What does the set
{
x
∣
x
>
−
4
}
\{x | x > -4\}
{
x
∣
x
>
−
4
}
represent?
\newline
Choices:
\newline
(A)all numbers less than
−
4
-4
−
4
\newline
(B)all numbers greater than
−
4
-4
−
4
\newline
(C)all numbers greater than or equal to
−
4
-4
−
4
\newline
(D)all numbers less than or equal to
−
4
-4
−
4
Get tutor help
What does the set
{
x
∣
x
≥
−
15
}
\{x | x \geq -15\}
{
x
∣
x
≥
−
15
}
represent?
\newline
Choices:
\newline
(A)all numbers less than
−
15
-15
−
15
\newline
(B)all numbers greater than
−
15
-15
−
15
\newline
(C)all numbers greater than or equal to
−
15
-15
−
15
\newline
(D)all numbers equal to
−
15
-15
−
15
Get tutor help
Which of the following is a rational number?
\newline
Choices:
\newline
(A)
8
9
\frac{8}{9}
9
8
\newline
(B)
3
\sqrt{3}
3
\newline
(C)
π
\pi
π
\newline
(D)
2
\sqrt{2}
2
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Which of the following are whole numbers?
\newline
Multi-select Choices:
\newline
(A)
0
0
0
\newline
(B)
π
\pi
π
\newline
(C)
−
3
-3
−
3
\newline
(D)
6
\sqrt{6}
6
Get tutor help
Which of the following are natural numbers?
\newline
Multi-select Choices:
\newline
(A)
3
3
3
\newline
(B)
3
\sqrt{3}
3
\newline
(C)
π
\pi
π
\newline
(D)
9
9
9
Get tutor help
Which of the following are real numbers?
\newline
Multi-select Choices:
\newline
(A)
5
\sqrt{5}
5
\newline
(B)
π
\pi
π
\newline
(C)
1
2
\frac{1}{2}
2
1
\newline
(D)
0
0
0
Get tutor help
Which of the following are irrational numbers?
\newline
Multi-select Choices:
\newline
(A)
5
5
5
\newline
(B)
2
2
2
\newline
(C)
6
\sqrt{6}
6
\newline
(D)
5
\sqrt{5}
5
Get tutor help
Suppose that the function
h
h
h
is defined, for all real numbers, as follows.
\newline
h
(
x
)
=
{
1
2
x
−
2
if
x
≤
−
2
−
(
x
+
1
)
2
if
−
2
<
x
≤
1
−
1
if
x
>
1
h(x)=\left\{\begin{array}{ll} \frac{1}{2} x-2 & \text { if } x \leq-2 \\ -(x+1)^{2} & \text { if }-2<x \leq 1 \\ -1 & \text { if } x>1 \end{array}\right.
h
(
x
)
=
⎩
⎨
⎧
2
1
x
−
2
−
(
x
+
1
)
2
−
1
if
x
≤
−
2
if
−
2
<
x
≤
1
if
x
>
1
\newline
Find
h
(
−
3
)
,
h
(
−
1
)
h(-3), h(-1)
h
(
−
3
)
,
h
(
−
1
)
, and
h
(
1
)
h(1)
h
(
1
)
.
\newline
h
(
−
3
)
=
h
(
−
1
)
=
h
(
1
)
=
\begin{array}{l} h(-3)= \\ h(-1)= \\ h(1)= \end{array}
h
(
−
3
)
=
h
(
−
1
)
=
h
(
1
)
=
Get tutor help
Find the argument of the complex number
−
8
−
7
i
-8-7 i
−
8
−
7
i
in the interval
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, rounding to the nearest tenth of a degree if necessary.
Get tutor help
The number of real values of
a
a
a
satisfying the equation
a
2
−
2
a
sin
x
+
1
=
0
a^{2}-2a \sin x+1=0
a
2
−
2
a
sin
x
+
1
=
0
is
Get tutor help
Which of the following describe
3
p
3p
3
p
?
\newline
Select all that apply.
\newline
(1) Real number
\newline
(2) Integer
\newline
(3) Whole number
\newline
(4) Natural number
\newline
(5) Number
Get tutor help
Which of the following are rational numbers?
\newline
Multi-select Choices:
\newline
(A)
1
7
\frac{1}{7}
7
1
\newline
(B)
0
0
0
\newline
(C)
9.81
9.81
9.81
\newline
(D)
9
4
\frac{9}{4}
4
9
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x
<
3
x<3
x
<
3
in Interval Notation is
(
∞
,
3
)
(\infty, 3)
(
∞
,
3
)
\newline
True
\newline
False
Get tutor help
f
g
(
x
)
=
11
x
+
2
x
2
−
7
x
−
3
x
2
+
4
\frac{f}{g}(x) = \frac{11x + 2x^2}{-7x - 3x^2 + 4}
g
f
(
x
)
=
−
7
x
−
3
x
2
+
4
11
x
+
2
x
2
Find the domain
Get tutor help
Let
h
h
h
be a continuous function on the closed interval
[
0
,
4
]
[0,4]
[
0
,
4
]
, where
h
(
0
)
=
2
h(0)=2
h
(
0
)
=
2
and
h
(
4
)
=
−
2
h(4)=-2
h
(
4
)
=
−
2
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
h
(
c
)
=
−
1
h(c)=-1
h
(
c
)
=
−
1
for at least one
c
c
c
between
−
2
-2
−
2
and
2
2
2
\newline
(B)
h
(
c
)
=
3
h(c)=3
h
(
c
)
=
3
for at least one
c
c
c
between
−
2
-2
−
2
and
2
2
2
\newline
(C)
h
(
c
)
=
−
1
h(c)=-1
h
(
c
)
=
−
1
for at least one
c
c
c
between
0
0
0
and
4
4
4
\newline
(D)
h
(
c
)
=
3
h(c)=3
h
(
c
)
=
3
for at least one
c
c
c
between
0
0
0
and
4
4
4
Get tutor help
Let
f
f
f
be a continuous function on the closed interval
[
1
,
5
]
[1,5]
[
1
,
5
]
, where
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
5
)
=
−
3
f(5)=-3
f
(
5
)
=
−
3
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
c
)
=
−
2
f(c)=-2
f
(
c
)
=
−
2
for at least one
c
c
c
between
1
1
1
and
5
5
5
\newline
(B)
f
(
c
)
=
−
2
f(c)=-2
f
(
c
)
=
−
2
for at least one
c
c
c
between
−
3
-3
−
3
and
1
1
1
\newline
(C)
f
(
c
)
=
2
f(c)=2
f
(
c
)
=
2
for at least one
c
c
c
between
1
1
1
and
5
5
5
\newline
(D)
f
(
c
)
=
2
f(c)=2
f
(
c
)
=
2
for at least one
c
c
c
between
−
3
-3
−
3
and
1
1
1
Get tutor help
Which of the following functions are continuous for all real numbers?
\newline
g
(
x
)
=
2
x
g(x)=2^{x}
g
(
x
)
=
2
x
\newline
f
(
x
)
=
ln
(
x
)
f(x)=\ln (x)
f
(
x
)
=
ln
(
x
)
\newline
Choose
1
1
1
answer:
\newline
(A)
g
g
g
only
\newline
(B)
f
f
f
only
\newline
(C) Both
g
g
g
and
f
f
f
\newline
(D) Neither
g
g
g
nor
f
f
f
Get tutor help
Which of the following functions are continuous at
x
=
0
x=0
x
=
0
?
\newline
g
(
x
)
=
cot
(
x
)
g(x)=\cot (x)
g
(
x
)
=
cot
(
x
)
\newline
h
(
x
)
=
1
x
2
h(x)=\frac{1}{x^{2}}
h
(
x
)
=
x
2
1
\newline
Choose
1
1
1
answer:
\newline
(A)
g
g
g
only
\newline
(B)
h
h
h
only
\newline
(C) Both
g
g
g
and
h
h
h
\newline
(D) Neither
g
g
g
nor
h
h
h
Get tutor help
Which of the following functions are continuous for all real numbers?
\newline
h
(
x
)
=
1
x
2
h(x)=\frac{1}{x^{2}}
h
(
x
)
=
x
2
1
\newline
g
(
x
)
=
x
2
g(x)=x^{2}
g
(
x
)
=
x
2
\newline
Choose
1
1
1
answer:
\newline
(A)
h
h
h
only
\newline
(B)
g
g
g
only
\newline
(C) Both
h
h
h
and
g
g
g
\newline
(D) Neither
h
h
h
nor
g
g
g
Get tutor help
Which of the following functions are continuous for all real numbers?
\newline
f
(
x
)
=
tan
(
x
)
h
(
x
)
=
x
3
\begin{array}{l} f(x)=\tan (x) \\ h(x)=x^{3} \end{array}
f
(
x
)
=
tan
(
x
)
h
(
x
)
=
x
3
\newline
Choose
1
1
1
answer:
\newline
(A)
f
f
f
only
\newline
(B)
h
h
h
only
\newline
(C) Both
f
f
f
and
h
h
h
\newline
(D) Neither
f
f
f
nor
h
h
h
Get tutor help
Let
g
(
x
)
=
10
x
x
3
+
5
x
g(x)=\frac{10 x}{x^{3}+5 x}
g
(
x
)
=
x
3
+
5
x
10
x
when
x
≠
0
x \neq 0
x
=
0
.
\newline
g
g
g
is continuous for all real numbers.
\newline
Find
g
(
0
)
g(0)
g
(
0
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
2
2
2
\newline
(C)
5
5
5
\newline
(D)
10
\mathbf{1 0}
10
Get tutor help
Let
h
(
x
)
=
{
3
x
x
e
x
for
x
≠
0
k
for
x
=
0
h(x)=\left\{\begin{array}{ll}\frac{3 x}{x e^{x}} & \text { for } x \neq 0 \\ k & \text { for } x=0\end{array}\right.
h
(
x
)
=
{
x
e
x
3
x
k
for
x
=
0
for
x
=
0
\newline
h
h
h
is continuous for all real numbers.
\newline
What is the value of
k
k
k
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
3
3
3
\newline
(D)
e
e
e
Get tutor help
Let
h
(
x
)
=
x
2
−
49
x
+
7
h(x)=\frac{x^{2}-49}{x+7}
h
(
x
)
=
x
+
7
x
2
−
49
when
x
≠
−
7
x \neq-7
x
=
−
7
.
\newline
h
h
h
is continuous for all real numbers.
\newline
Find
h
(
−
7
)
h(-7)
h
(
−
7
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
-7
−
7
\newline
(B)
14
14
14
\newline
(C)
7
7
7
\newline
(D)
−
14
-14
−
14
Get tutor help
Let
g
(
x
)
=
x
2
−
x
−
12
x
−
4
g(x)=\frac{x^{2}-x-12}{x-4}
g
(
x
)
=
x
−
4
x
2
−
x
−
12
when
x
≠
4
x \neq 4
x
=
4
.
\newline
g
g
g
is continuous for all real numbers.
\newline
Find
g
(
4
)
g(4)
g
(
4
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
4
-4
−
4
\newline
(B)
−
3
-3
−
3
\newline
(C)
4
4
4
\newline
(D)
7
7
7
Get tutor help
Let
f
(
x
)
=
x
+
1
x
e
x
+
e
x
f(x)=\frac{x+1}{x e^{x}+e^{x}}
f
(
x
)
=
x
e
x
+
e
x
x
+
1
when
x
≠
−
1
x \neq-1
x
=
−
1
.
\newline
f
f
f
is continuous for all real numbers.
\newline
Find
f
(
−
1
)
f(-1)
f
(
−
1
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
e
-2 e
−
2
e
\newline
(B)
1
1
1
\newline
(C)
e
e
e
\newline
(D)
2
2
2
Get tutor help
Which of the following is equivalent to the complex number
i
17
i^{17}
i
17
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
54
i^{54}
i
54
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
30
i^{30}
i
30
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
5
i^{5}
i
5
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
41
i^{41}
i
41
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
20
i^{20}
i
20
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
32
i^{32}
i
32
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
14
i^{14}
i
14
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
38
i^{38}
i
38
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
10
i^{10}
i
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
8
i^{8}
i
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
24
i^{24}
i
24
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
9
i^{9}
i
9
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
36
i^{36}
i
36
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
31
i^{31}
i
31
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
11
i^{11}
i
11
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
15
i^{15}
i
15
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
35
i^{35}
i
35
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
51
i^{51}
i
51
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
19
i^{19}
i
19
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Which of the following is equivalent to the complex number
i
28
i^{28}
i
28
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
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