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Math Problems
Algebra 1
Domain and range of quadratic functions: equations
Which of the following functions are continuous for all real numbers?
\newline
g
(
x
)
=
x
5
g(x) = \sqrt[5]{x}
g
(
x
)
=
5
x
\newline
h
(
x
)
=
x
3
h(x) = \sqrt[3]{x}
h
(
x
)
=
3
x
\newline
Choose
1
1
1
answer:
\newline
(Choice A)
g
g
g
only
\newline
(Choice B)
h
h
h
only
\newline
(Choice C) Both
g
g
g
and
h
h
h
\newline
(Choice D) Neither
g
g
g
nor
h
h
h
Get tutor help
The table below shows some inputs and outputs of the invertible function with domain all real numbers.
x
x
x
5
5
5
3
3
3
1
1
1
18
18
18
0
0
0
9
9
9
f
(
x
)
f(x)
f
(
x
)
9
9
9
−
2
-2
−
2
−
5
-5
−
5
−
1
-1
−
1
1
1
1
11
11
11
Get tutor help
Ver en espa\~{n}ol Maddie takes piano lessons at River Rock Arts Center, where she pays
$
25
\$25
$25
per lesson. The function
C
(
p
)
C(p)
C
(
p
)
represents the cost, in dollars, of
p
p
p
piano lessons. What is the domain of
C
(
p
)
C(p)
C
(
p
)
?
\newline
a) All Real Numbers
\newline
b) all real numbers
0
0
0
to
25
25
25
\newline
c) a whole number
0
0
0
to
25
25
25
\newline
d) all real numbers
Get tutor help
For each function, state whether it is linear, quadratic, or exponential.
\newline
\newline
Function
1
1
1
\newline
Function
2
2
2
\newline
Function
3
3
3
\newline
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
\newline
3
3
3
\newline
35
35
35
\newline
1
1
1
\newline
9
9
9
\newline
y
y
y
0
0
0
\newline
y
y
y
1
1
1
\newline
\newline
y
y
y
2
2
2
\newline
y
y
y
3
3
3
\newline
y
y
y
0
0
0
\newline
y
y
y
5
5
5
\newline
3
3
3
\newline
y
y
y
7
7
7
\newline
\newline
y
y
y
8
8
8
\newline
y
y
y
9
9
9
\newline
3
3
3
\newline
9
9
9
\newline
y
y
y
2
2
2
\newline
x
x
x
3
3
3
\newline
\newline
x
x
x
4
4
4
\newline
x
x
x
5
5
5
\newline
\bar{
4
4
4
}\(\newline\)\(x\)\(6\)\(\newline\)\bar{\(5\)}
\newline
\newline
y
y
y
5
5
5
\newline
x
x
x
8
8
8
\newline
x
x
x
9
9
9
\newline
y
y
y
3
3
3
\newline
\bar{
6
6
6
}$\(\newline\)\(y\)\(1\)\(\newline\)\(\newline\)Linear\(\newline\)Linear\(\newline\)Linear\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Exponential\(\newline\)Exponential\(\newline\)Exponential\(\newline\)None of the above\(\newline\)None of the above\(\newline\)None of the above
Get tutor help
Find the domain of the function
f
(
x
)
=
1
2
−
2
x
−
x
2
f(x)=\frac{1}{\sqrt{2-2 x-x^{2}}}
f
(
x
)
=
2
−
2
x
−
x
2
1
. (Enter your answer using interval notation.)
Get tutor help
f
(
x
)
=
(
5
x
+
3
)
(
x
−
2
)
(
3
x
+
7
)
(
x
+
5
)
f(x)=(5 x+3)(x-2)(3 x+7)(x+5)
f
(
x
)
=
(
5
x
+
3
)
(
x
−
2
)
(
3
x
+
7
)
(
x
+
5
)
has zeros at
x
=
−
5
,
x
=
−
7
3
,
x
=
−
3
5
x=-5, x=-\frac{7}{3}, x=-\frac{3}{5}
x
=
−
5
,
x
=
−
3
7
,
x
=
−
5
3
, and
x
=
2
x=2
x
=
2
.
\newline
What is the sign of
f
f
f
on the interval
−
7
3
<
x
<
−
3
5
-\frac{7}{3}<x<-\frac{3}{5}
−
3
7
<
x
<
−
5
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
f
f
is always positive on the interval.
\newline
(B)
f
f
f
is always negative on the interval.
\newline
(C)
f
f
f
is sometimes positive and sometimes negative on the interval.
Get tutor help
The function
f
f
f
is defined as
f
(
x
)
=
x
2
−
1
f(x)=x^{2}-1
f
(
x
)
=
x
2
−
1
.
\newline
What is the
x
x
x
-coordinate of the point on the function's graph that is closest to the origin?
\newline
Choose all answers that apply:
\newline
A
−
3
3
-\frac{\sqrt{3}}{3}
−
3
3
\newline
B
−
2
2
-\frac{\sqrt{2}}{2}
−
2
2
\newline
c
0
0
0
\newline
D
3
3
\frac{\sqrt{3}}{3}
3
3
\newline
E
2
2
\frac{\sqrt{2}}{2}
2
2
Get tutor help
The set
S
=
{
x
∣
−
3
<
x
<
4
}
S=\{x \mid-3<x<4\}
S
=
{
x
∣
−
3
<
x
<
4
}
is described by which interval notation?
\newline
[
−
3
,
4
]
[-3,4]
[
−
3
,
4
]
\newline
(
−
3
,
4
]
(-3,4]
(
−
3
,
4
]
\newline
[
−
3
,
4
[-3,4
[
−
3
,
4
)
\newline
(
−
3
,
4
)
(-3,4)
(
−
3
,
4
)
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
16
x
+
64
y = x^2 - 16x + 64
y
=
x
2
−
16
x
+
64
\newline
Choices:
\newline
(A)
x
∣
x
≥
8
{x | x \geq 8}
x
∣
x
≥
8
\newline
(B)
x
∣
x
≤
8
{x | x \leq 8}
x
∣
x
≤
8
\newline
(C)
x
∣
x
≥
0
{x | x \geq 0}
x
∣
x
≥
0
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
4
x
+
4
y = x^2 + 4x + 4
y
=
x
2
+
4
x
+
4
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
2
{y | y \geq -2}
y
∣
y
≥
−
2
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
2
x
+
1
y = x^2 - 2x + 1
y
=
x
2
−
2
x
+
1
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
1
}
\{x | x \leq 1\}
{
x
∣
x
≤
1
}
\newline
(B)
{
x
∣
x
≥
1
}
\{x | x \geq 1\}
{
x
∣
x
≥
1
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
12
x
+
36
y = x^2 - 12x + 36
y
=
x
2
−
12
x
+
36
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(B)
{
x
∣
x
≥
6
}
\{x | x \geq 6\}
{
x
∣
x
≥
6
}
\newline
(C)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
2
x
−
24
y = x^2 + 2x - 24
y
=
x
2
+
2
x
−
24
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
25
}
\{x | x \geq -25\}
{
x
∣
x
≥
−
25
}
\newline
(B)
{
x
∣
x
≤
−
1
}
\{x | x \leq -1\}
{
x
∣
x
≤
−
1
}
\newline
(C)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
6
x
+
9
y = x^2 - 6x + 9
y
=
x
2
−
6
x
+
9
\newline
Choices:
\newline
(A)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≥
−
3
{y | y \geq -3}
y
∣
y
≥
−
3
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
2
x
−
15
y = x^2 - 2x - 15
y
=
x
2
−
2
x
−
15
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
1
}
\{x | x \leq 1\}
{
x
∣
x
≤
1
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≥
−
16
}
\{x | x \geq -16\}
{
x
∣
x
≥
−
16
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
4
y = x^2 - 4
y
=
x
2
−
4
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(B)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(C)
{
x
∣
x
≥
−
4
}
\{x | x \geq -4\}
{
x
∣
x
≥
−
4
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
12
x
+
20
y = x^2 + 12x + 20
y
=
x
2
+
12
x
+
20
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
6
}
\{y | y \leq -6\}
{
y
∣
y
≤
−
6
}
\newline
(B)
{
y
∣
y
≥
−
6
}
\{y | y \geq -6\}
{
y
∣
y
≥
−
6
}
\newline
(C)
{
y
∣
y
≥
−
16
}
\{y | y \geq -16\}
{
y
∣
y
≥
−
16
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
32
y = x^2 - 12x + 32
y
=
x
2
−
12
x
+
32
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(B)
y
∣
y
≥
4
{y | y \geq 4}
y
∣
y
≥
4
\newline
(C)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
35
y = x^2 + 2x - 35
y
=
x
2
+
2
x
−
35
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
1
}
\{y | y \leq -1\}
{
y
∣
y
≤
−
1
}
\newline
(B)
{
y
∣
y
≥
−
1
}
\{y | y \geq -1\}
{
y
∣
y
≥
−
1
}
\newline
(C)
{
y
∣
y
≥
−
36
}
\{y | y \geq -36\}
{
y
∣
y
≥
−
36
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
16
x
+
64
y = x^2 + 16x + 64
y
=
x
2
+
16
x
+
64
\newline
Choices:
\newline
(A)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≥
−
8
{y | y \geq -8}
y
∣
y
≥
−
8
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
10
x
+
24
y = x^2 + 10x + 24
y
=
x
2
+
10
x
+
24
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(B)
{
x
∣
x
≥
−
5
}
\{x | x \geq -5\}
{
x
∣
x
≥
−
5
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
8
x
−
20
y = x^2 - 8x - 20
y
=
x
2
−
8
x
−
20
\newline
Choices:
\newline
(A)
x
∣
x
≥
−
36
{x | x \geq -36}
x
∣
x
≥
−
36
\newline
(B)
x
∣
x
≤
4
{x | x \leq 4}
x
∣
x
≤
4
\newline
(C)
x
∣
x
≥
0
{x | x \geq 0}
x
∣
x
≥
0
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
35
y = x^2 - 12x + 35
y
=
x
2
−
12
x
+
35
\newline
Choices:
\newline
(A)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(B)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(C)
y
∣
y
≤
−
1
{y | y \leq -1}
y
∣
y
≤
−
1
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
27
y = x^2 - 12x + 27
y
=
x
2
−
12
x
+
27
\newline
Choices:
\newline
(A)
y
∣
y
≥
9
{y | y \geq 9}
y
∣
y
≥
9
\newline
(B)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(C)
y
∣
y
≥
−
9
{y | y \geq -9}
y
∣
y
≥
−
9
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
14
x
+
49
y = x^2 - 14x + 49
y
=
x
2
−
14
x
+
49
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
7
}
\{y | y \leq -7\}
{
y
∣
y
≤
−
7
}
\newline
(B)
{
y
∣
y
≥
−
7
}
\{y | y \geq -7\}
{
y
∣
y
≥
−
7
}
\newline
(C)
{
y
∣
y
≥
0
}
\{y | y \geq 0\}
{
y
∣
y
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
15
y = x^2 + 2x - 15
y
=
x
2
+
2
x
−
15
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
16
{y | y \geq -16}
y
∣
y
≥
−
16
\newline
(B)
y
∣
y
≤
−
16
{y | y \leq -16}
y
∣
y
≤
−
16
\newline
(C)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
14
x
+
49
y = x^2 + 14x + 49
y
=
x
2
+
14
x
+
49
\newline
Choices:
\newline
(A)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
−
7
{y | y \geq -7}
y
∣
y
≥
−
7
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
10
x
+
25
y = x^2 - 10x + 25
y
=
x
2
−
10
x
+
25
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
5
}
\{x | x \geq 5\}
{
x
∣
x
≥
5
}
\newline
(B)
{
x
∣
x
≤
5
}
\{x | x \leq 5\}
{
x
∣
x
≤
5
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
12
x
+
36
y = x^2 + 12x + 36
y
=
x
2
+
12
x
+
36
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≥
−
6
}
\{x | x \geq -6\}
{
x
∣
x
≥
−
6
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
4
x
+
4
y = x^2 - 4x + 4
y
=
x
2
−
4
x
+
4
\newline
Choices:
\newline
(A)
y
∣
y
≥
2
{y | y \geq 2}
y
∣
y
≥
2
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
2
x
−
24
y = x^2 - 2x - 24
y
=
x
2
−
2
x
−
24
\newline
Choices:
\newline
(A)
y
∣
y
≤
−
25
{y | y \leq -25}
y
∣
y
≤
−
25
\newline
(B)
y
∣
y
≥
1
{y | y \geq 1}
y
∣
y
≥
1
\newline
(C)
y
∣
y
≥
−
25
{y | y \geq -25}
y
∣
y
≥
−
25
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
+
1
y = x^2 + 2x + 1
y
=
x
2
+
2
x
+
1
\newline
Choices:
\newline
(A)
y
∣
y
≥
1
{y | y \geq 1}
y
∣
y
≥
1
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
6
x
−
40
y = x^2 - 6x - 40
y
=
x
2
−
6
x
−
40
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
3
}
\{x | x \leq 3\}
{
x
∣
x
≤
3
}
\newline
(B)
{
x
∣
x
≥
3
}
\{x | x \geq 3\}
{
x
∣
x
≥
3
}
\newline
(C)
{
x
∣
x
≥
−
49
}
\{x | x \geq -49\}
{
x
∣
x
≥
−
49
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
6
x
+
8
y = x^2 - 6x + 8
y
=
x
2
−
6
x
+
8
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
3
}
\{x | x \leq 3\}
{
x
∣
x
≤
3
}
\newline
(B)
{
x
∣
x
≥
3
}
\{x | x \geq 3\}
{
x
∣
x
≥
3
}
\newline
(C)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
8
x
+
16
y = x^2 - 8x + 16
y
=
x
2
−
8
x
+
16
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
4
}
\{x | x \geq 4\}
{
x
∣
x
≥
4
}
\newline
(B)
{
x
∣
x
≤
4
}
\{x | x \leq 4\}
{
x
∣
x
≤
4
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
8
x
+
12
y = x^2 - 8x + 12
y
=
x
2
−
8
x
+
12
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
4
}
\{y | y \leq -4\}
{
y
∣
y
≤
−
4
}
\newline
(B)
{
y
∣
y
≥
4
}
\{y | y \geq 4\}
{
y
∣
y
≥
4
}
\newline
(C)
{
y
∣
y
≥
−
4
}
\{y | y \geq -4\}
{
y
∣
y
≥
−
4
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
3
y = x^2 + 2x - 3
y
=
x
2
+
2
x
−
3
\newline
Choices:
\newline
(A)
y
∣
y
≥
4
{y | y \geq 4}
y
∣
y
≥
4
\newline
(B)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(C)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
6
x
+
9
y = x^2 + 6x + 9
y
=
x
2
+
6
x
+
9
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
3
}
\{x | x \geq -3\}
{
x
∣
x
≥
−
3
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≤
−
3
}
\{x | x \leq -3\}
{
x
∣
x
≤
−
3
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
4
x
+
3
y = x^2 - 4x + 3
y
=
x
2
−
4
x
+
3
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(B)
{
x
∣
x
≥
2
}
\{x | x \geq 2\}
{
x
∣
x
≥
2
}
\newline
(C)
{
x
∣
x
≤
2
}
\{x | x \leq 2\}
{
x
∣
x
≤
2
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
4
x
−
12
y = x^2 - 4x - 12
y
=
x
2
−
4
x
−
12
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
16
{y | y \geq -16}
y
∣
y
≥
−
16
\newline
(B)
y
∣
y
≥
2
{y | y \geq 2}
y
∣
y
≥
2
\newline
(C)
y
∣
y
≥
16
{y | y \geq 16}
y
∣
y
≥
16
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
8
x
+
16
y = x^2 + 8x + 16
y
=
x
2
+
8
x
+
16
\newline
Choices:
\newline
(A)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(D)all real numbers
Get tutor help
Consider the function
h
(
x
)
=
−
(
2
sin
(
1
−
x
)
+
8
)
h(x) = -(2\sin(1-x) + 8)
h
(
x
)
=
−
(
2
sin
(
1
−
x
)
+
8
)
.
\newline
Giving your answer in interval notation, find the domain of
h
−
1
(
x
)
h^{-1}(x)
h
−
1
(
x
)
.
Get tutor help
Consider the function
h
(
x
)
=
−
(
2
sin
(
1
−
x
)
+
8
)
h(x)=-(2 \sin (1-x)+8)
h
(
x
)
=
−
(
2
sin
(
1
−
x
)
+
8
)
.
\newline
Giving your answer in interval notation, find the domain of
h
−
1
(
x
)
h^{-1}(x)
h
−
1
(
x
)
.
Get tutor help
Helen has a remote-control boat that she drives in a pond at Blake Park. The boat has a maximum speed of
8
8
8
meters per second. She accelerates the boat to its maximum speed and drives it for
1
1
1
minute around the pond before decelerating. The function
D
(
t
)
D(t)
D
(
t
)
represents the distance the boat has traveled at maximum speed after
t
t
t
seconds.
\newline
What is the domain of
D
(
t
)
D(t)
D
(
t
)
?
\newline
Choices:
\newline
(A)all multiples of
8
8
8
\newline
(B)all real numbers less than
60
60
60
\newline
(C)all real numbers from
0
0
0
to
60
60
60
\newline
(D)all whole numbers from
0
0
0
to
8
8
8
Get tutor help
Stefan works as a pizza chef. He begins his day by preheating the pizza oven. Today, the oven's interior temperature was
72
°
F
72\degree\text{F}
72°
F
when Stefan turned it on high-power to preheat. The temperature rose steadily at a rate of
12
°
F
12\degree\text{F}
12°
F
per minute until it reached its ideal temperature an hour later. Then, Stefan reduced the power so the temperature would stop rising. The function
T
(
m
)
T(m)
T
(
m
)
represents the oven's interior temperature, in
°
F
\degree\text{F}
°
F
, after
m
m
m
minutes of preheating.
\newline
What is the domain of
T
(
m
)
T(m)
T
(
m
)
?
\newline
Choices:
\newline
(A)all real numbers from
0
0
0
to
72
72
72
\newline
(B)all whole numbers greater than or equal to
72
72
72
\newline
(C)all real numbers from
0
0
0
to
12
°
F
12\degree\text{F}
12°
F
0
0
0
\newline
(D)all whole numbers less than or equal to
12
°
F
12\degree\text{F}
12°
F
1
1
1
Get tutor help
Stefan works as a pizza chef. He begins his day by preheating the pizza oven. Today, the oven's interior temperature was
72
°
F
72\degree\text{F}
72°
F
when Stefan turned it on high-power to preheat. The temperature rose steadily at a rate of
12
°
F
12\degree\text{F}
12°
F
per minute until it reached its ideal temperature an hour later. Then, Stefan reduced the power so the temperature would stop rising. The function
T
(
m
)
T(m)
T
(
m
)
represents the oven's interior temperature, in
°
F
\degree\text{F}
°
F
, after
m
m
m
minutes of preheating.
\newline
What is the domain of
T
(
m
)
T(m)
T
(
m
)
?
\newline
(A) all whole numbers greater than or equal to
72
72
72
\newline
(B) all real numbers from
0
0
0
to
72
72
72
\newline
(C) all whole numbers less than or equal to
12
12
12
\newline
(D) all real numbers from
0
0
0
to
12
°
F
12\degree\text{F}
12°
F
1
1
1
Get tutor help
Today, Madelyn is running a
10
10
10
-mile race and using her watch to help with pacing. She will run at a steady pace of
9
9
9
minutes per mile, and so she expects to finish the race in
90
90
90
minutes. The function
D
(
m
)
D(m)
D
(
m
)
represents the distance Madelyn has left to run, in miles, after
m
m
m
minutes.
\newline
What is the domain of
D
(
m
)
D(m)
D
(
m
)
?
\newline
Choices:
\newline
(A)all real numbers from
0
0
0
to
10
10
10
\newline
(B)all whole numbers from
0
0
0
to
90
90
90
\newline
(C)all whole numbers from
0
0
0
to
10
10
10
\newline
(D)all real numbers from
0
0
0
to
90
90
90
Get tutor help
find the range of
k
k
k
for the equation
x
2
−
2
k
x
+
k
2
−
2
k
=
6
x^2 - 2kx + k^2 - 2k = 6
x
2
−
2
k
x
+
k
2
−
2
k
=
6
has real roots. Find the roots in terms of
k
k
k
Get tutor help
What does the set
{
x
∣
x
>
−
4
}
\{x | x > -4\}
{
x
∣
x
>
−
4
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than or equal to
−
4
-4
−
4
\newline
(B)all numbers less than or equal to
−
4
-4
−
4
\newline
(C)all numbers less than
−
4
-4
−
4
\newline
(D)all numbers greater than
−
4
-4
−
4
Get tutor help
What does the set
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
represent?
\newline
Choices:
\newline
(A)all numbers greater than or equal to
0
0
0
\newline
(B)all numbers less than or equal to
0
0
0
\newline
(C)all numbers greater than
0
0
0
\newline
(D)all numbers equal to
0
0
0
Get tutor help
1
2
3
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