Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 1
Domain and range of quadratic functions: equations
Which of the following is equivalent to the complex number
i
22
i^{22}
i
22
?
\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
6
i^{6}
i
6
?
\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
16
i^{16}
i
16
?
\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
34
i^{34}
i
34
?
\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
80
i^{80}
i
80
?
\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
13
i^{13}
i
13
?
\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
7
i^{7}
i
7
?
\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
What is the amplitude of
g
(
x
)
=
10
cos
(
6
x
−
1
)
−
4
g(x)=10 \cos (6 x-1)-4
g
(
x
)
=
10
cos
(
6
x
−
1
)
−
4
?
\newline
units
Get tutor help
What is the period of the function
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
h(x)=-3 \cos (\pi x+2)-6 ?
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
\newline
h
(
x
)
=
5
sin
(
4
x
−
2
)
−
3
?
h(x)=5 \sin (4 x-2)-3 \text { ? }
h
(
x
)
=
5
sin
(
4
x
−
2
)
−
3
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
g
(
x
)
=
2
cos
(
7
x
+
5
)
+
1
?
g(x)=2 \cos (7 x+5)+1 ?
g
(
x
)
=
2
cos
(
7
x
+
5
)
+
1
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
g
(
x
)
=
−
sin
(
−
8
x
−
3
)
+
5
?
g(x)=-\sin (-8 x-3)+5 ?
g
(
x
)
=
−
sin
(
−
8
x
−
3
)
+
5
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
\newline
g
(
x
)
=
−
9
cos
(
−
π
2
x
−
6
)
+
8
?
g(x)=-9 \cos \left(-\frac{\pi}{2} x-6\right)+8 ?
g
(
x
)
=
−
9
cos
(
−
2
π
x
−
6
)
+
8
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
f
(
x
)
=
−
6
sin
(
3
π
x
+
4
)
−
2
f(x)=-6 \sin (3 \pi x+4)-2
f
(
x
)
=
−
6
sin
(
3
π
x
+
4
)
−
2
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
f
(
x
)
=
3
sin
(
2
x
−
1
)
+
4
f(x)=3 \sin (2 x-1)+4
f
(
x
)
=
3
sin
(
2
x
−
1
)
+
4
?
\newline
Give an exact value.
\newline
units
Get tutor help
What is the period of the function
f
(
x
)
=
−
4
cos
(
5
x
−
9
)
−
7
f(x)=-4 \cos (5 x-9)-7
f
(
x
)
=
−
4
cos
(
5
x
−
9
)
−
7
?
\newline
Give an exact value.
\newline
units
Get tutor help
y
=
(
x
−
2
)
(
x
+
4
)
y=(x-2)(x+4)
y
=
(
x
−
2
)
(
x
+
4
)
\newline
The given equation represents a parabola in the
x
y
x y
x
y
-plane. Which of the following equivalent forms of the equation displays the coordinates of the vertex of the parabola as constants or coefficients?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
x
2
+
2
x
−
8
y=x^{2}+2 x-8
y
=
x
2
+
2
x
−
8
\newline
(B)
y
=
(
x
+
1
)
2
−
9
y=(x+1)^{2}-9
y
=
(
x
+
1
)
2
−
9
\newline
(C)
y
−
40
=
(
x
−
6
)
(
x
+
8
)
y-40=(x-6)(x+8)
y
−
40
=
(
x
−
6
)
(
x
+
8
)
\newline
(D)
y
+
5
=
(
x
−
1
)
(
x
+
3
)
y+5=(x-1)(x+3)
y
+
5
=
(
x
−
1
)
(
x
+
3
)
Get tutor help
f
(
x
)
=
−
(
x
+
1
)
(
x
+
7
)
f(x)=-(x+1)(x+7)
f
(
x
)
=
−
(
x
+
1
)
(
x
+
7
)
\newline
The function represents a parabola in the
x
y
x y
x
y
-plane. Which of the following is an equivalent form of
f
f
f
in which the
y
y
y
-intercept of the graph of
f
f
f
appears as a constant or coefficient?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
x
)
=
−
(
x
+
4
)
2
+
9
f(x)=-(x+4)^{2}+9
f
(
x
)
=
−
(
x
+
4
)
2
+
9
\newline
(B)
f
(
x
)
=
−
(
x
+
4
)
2
−
9
f(x)=-(x+4)^{2}-9
f
(
x
)
=
−
(
x
+
4
)
2
−
9
\newline
(C)
f
(
x
)
=
−
x
2
+
8
x
+
7
f(x)=-x^{2}+8 x+7
f
(
x
)
=
−
x
2
+
8
x
+
7
\newline
(D)
f
(
x
)
=
−
x
2
−
8
x
−
7
f(x)=-x^{2}-8 x-7
f
(
x
)
=
−
x
2
−
8
x
−
7
Get tutor help
y
=
x
2
+
4
x
−
21
y=x^{2}+4 x-21
y
=
x
2
+
4
x
−
21
\newline
The given equation represents a parabola in the
x
y
x y
x
y
-plane. Which of the following equivalent forms of the equation displays the
x
x
x
intercepts of the parabola as constants or coefficients?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
(
x
−
3
)
(
x
+
7
)
y=(x-3)(x+7)
y
=
(
x
−
3
)
(
x
+
7
)
\newline
(B)
y
=
x
(
x
+
4
)
−
21
y=x(x+4)-21
y
=
x
(
x
+
4
)
−
21
\newline
(C)
y
=
(
x
+
2
)
2
−
25
y=(x+2)^{2}-25
y
=
(
x
+
2
)
2
−
25
\newline
(D)
y
+
24
=
(
x
+
1
)
(
x
+
3
)
y+24=(x+1)(x+3)
y
+
24
=
(
x
+
1
)
(
x
+
3
)
Get tutor help
f
(
x
)
=
(
x
+
2
)
2
+
3
f(x)=(x+2)^{2}+3
f
(
x
)
=
(
x
+
2
)
2
+
3
\newline
The function represents a parabola in the
x
y
x y
x
y
-plane. Which of the following is an equivalent form of
f
f
f
in which the
y
y
y
-intercept of the graph of
f
f
f
appears as a constant or coefficient?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
x
)
=
x
2
+
4
x
+
3
f(x)=x^{2}+4 x+3
f
(
x
)
=
x
2
+
4
x
+
3
\newline
(B)
f
(
x
)
=
x
2
+
4
x
+
7
f(x)=x^{2}+4 x+7
f
(
x
)
=
x
2
+
4
x
+
7
\newline
(C)
f
(
x
)
=
(
x
+
1
)
(
x
+
3
)
⊣
f(x)=(x+1)(x+3) \dashv
f
(
x
)
=
(
x
+
1
)
(
x
+
3
)
⊣
\newline
(D)
f
(
x
)
=
(
x
+
2
)
(
x
+
5
)
f(x)=(x+2)(x+5)
f
(
x
)
=
(
x
+
2
)
(
x
+
5
)
Get tutor help
f
(
x
)
=
(
x
−
1
)
2
−
36
f(x)=(x-1)^{2}-36
f
(
x
)
=
(
x
−
1
)
2
−
36
\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
=
−
7
,
x
=
−
5
x=-7, x=-5
x
=
−
7
,
x
=
−
5
\newline
(B)
x
=
7
,
x
=
5
x=7, x=5
x
=
7
,
x
=
5
\newline
(C)
x
=
7
,
x
=
−
5
x=7, x=-5
x
=
7
,
x
=
−
5
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
Get tutor help
f
(
x
)
=
(
x
+
4
)
2
−
25
f(x)=(x+4)^{2}-25
f
(
x
)
=
(
x
+
4
)
2
−
25
\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
=
1
,
x
=
−
9
x=1, x=-9
x
=
1
,
x
=
−
9
\newline
(B)
x
=
1
,
x
=
9
x=1, x=9
x
=
1
,
x
=
9
\newline
(C)
x
=
−
1
,
x
=
−
9
x=-1, x=-9
x
=
−
1
,
x
=
−
9
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
Get tutor help
y
=
(
x
−
2
)
(
x
+
8
)
y=(x-2)(x+8)
y
=
(
x
−
2
)
(
x
+
8
)
\newline
The given equation represents a parabola in the
x
y
x y
x
y
-plane. Which of the following equivalent forms of the equation displays the
y
y
y
intercept of the parabola as a constant or coefficient?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
x
2
+
6
x
−
16
y=x^{2}+6 x-16
y
=
x
2
+
6
x
−
16
\newline
(B)
y
=
(
x
+
3
)
2
−
25
y=(x+3)^{2}-25
y
=
(
x
+
3
)
2
−
25
\newline
(C)
y
+
24
=
(
x
+
2
)
(
x
+
4
)
y+24=(x+2)(x+4)
y
+
24
=
(
x
+
2
)
(
x
+
4
)
\newline
(D)
y
+
25
=
(
x
+
3
)
2
y+25=(x+3)^{2}
y
+
25
=
(
x
+
3
)
2
Get tutor help
f
(
x
)
=
(
x
+
6
)
2
−
49
f(x)=(x+6)^{2}-49
f
(
x
)
=
(
x
+
6
)
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
=
1
,
x
=
13
x=1, x=13
x
=
1
,
x
=
13
\newline
(B)
x
=
−
1
,
x
=
−
13
x=-1, x=-13
x
=
−
1
,
x
=
−
13
\newline
(C)
x
=
1
,
x
=
−
13
x=1, x=-13
x
=
1
,
x
=
−
13
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
Get tutor help
f
(
x
)
=
(
x
−
8
)
2
−
9
f(x)=(x-8)^{2}-9
f
(
x
)
=
(
x
−
8
)
2
−
9
\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
=
−
11
,
x
=
5
x=-11, x=5
x
=
−
11
,
x
=
5
\newline
(B)
x
=
11
,
x
=
5
x=11, x=5
x
=
11
,
x
=
5
\newline
(C)
x
=
11
,
x
=
−
5
x=11, x=-5
x
=
11
,
x
=
−
5
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
Get tutor help
f
(
x
)
=
(
x
−
7
)
2
−
64
f(x)=(x-7)^{2}-64
f
(
x
)
=
(
x
−
7
)
2
−
64
\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
=
−
15
,
x
=
−
1
x=-15, x=-1
x
=
−
15
,
x
=
−
1
\newline
(B)
x
=
15
,
x
=
1
x=15, x=1
x
=
15
,
x
=
1
\newline
(C)
x
=
15
,
x
=
−
1
x=15, x=-1
x
=
15
,
x
=
−
1
\newline
(D)
f
(
x
)
f(x)
f
(
x
)
does not intersect the
x
x
x
-axis.
Get tutor help
Solve for
x
x
x
.
\newline
−
9
x
+
2
>
18
-9 x+2>18 \quad
−
9
x
+
2
>
18
AND
13
x
+
15
≤
−
4
\quad 13 x+15 \leq-4
13
x
+
15
≤
−
4
\newline
Choose
1
1
1
answer:
\newline
(A)
x
≤
−
19
13
x \leq-\frac{19}{13}
x
≤
−
13
19
\newline
(B)
x
<
−
16
9
x<-\frac{16}{9}
x
<
−
9
16
\newline
(C)
−
16
9
<
x
<
−
19
13
-\frac{16}{9}<x<-\frac{19}{13}
−
9
16
<
x
<
−
13
19
\newline
(D) There are no solutions
\newline
(E) All values of
x
x
x
are solutions
Get tutor help
Solve for
x
x
x
.
\newline
−
9
x
+
2
>
18
OR
13
x
+
15
≤
−
4
-9 x+2>18 \quad \text { OR } \quad 13 x+15 \leq-4
−
9
x
+
2
>
18
OR
13
x
+
15
≤
−
4
\newline
Choose
1
1
1
answer:
\newline
A)
x
≤
−
19
13
x \leq-\frac{19}{13}
x
≤
−
13
19
\newline
(B)
x
<
−
16
9
x<-\frac{16}{9}
x
<
−
9
16
\newline
(c)
−
16
9
<
x
<
−
19
13
-\frac{16}{9}<x<-\frac{19}{13}
−
9
16
<
x
<
−
13
19
\newline
(D) There are no solutions
\newline
(E) All values of
x
x
x
are solutions
Get tutor help
When graphed in the
x
y
x y
x
y
-plane, the function
f
(
x
)
=
3
(
2
)
x
+
1
f(x)=3(2)^{x}+1
f
(
x
)
=
3
(
2
)
x
+
1
has a
y
y
y
-intercept at
(
0
,
k
)
(0, k)
(
0
,
k
)
. What is the value of
k
k
k
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
2
2
2
\newline
(C)
3
3
3
\newline
(D)
4
4
4
Get tutor help
f
(
x
)
=
x
(
x
−
3
)
(
x
+
4
)
(
x
+
5
)
f(x)=x(x-3)(x+4)(x+5)
f
(
x
)
=
x
(
x
−
3
)
(
x
+
4
)
(
x
+
5
)
\newline
How many distinct zeroes does the function have?
Get tutor help
A polynomial function
M
M
M
is defined as
\newline
M
(
x
)
=
(
2
x
−
3
)
(
x
2
+
3
x
+
10
)
M(x)=(2 x-3)\left(x^{2}+3 x+10\right)
M
(
x
)
=
(
2
x
−
3
)
(
x
2
+
3
x
+
10
)
\newline
If
M
(
a
)
=
0
M(a)=0
M
(
a
)
=
0
for some real number
a
a
a
, then what is the value of
a
a
a
?
Get tutor help
If
y
=
(
x
−
1
)
(
x
+
5
)
y=(x-1)(x+5)
y
=
(
x
−
1
)
(
x
+
5
)
is graphed in the
x
y
x y
x
y
-plane, which of the following characteristics of the graph is displayed as a constant in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
x
x
-coordinate of the vertex
\newline
(B)
x
x
x
-intercept(s)
\newline
(C) Maximum
y
y
y
-value
\newline
(D)
y
y
y
-intercept
Get tutor help
The function
h
h
h
is defined over the real numbers. This table gives a few values of
h
h
h
.
\newline
\begin{tabular}{lllll}
\newline
x
x
x
&
−
6
-6
−
6
.
1
1
1
&
−
6
-6
−
6
.
01
01
01
&
−
6
-6
−
6
.
001
001
001
&
−
5
-5
−
5
.
9
9
9
\\
\newline
\hline
h
(
x
)
h(x)
h
(
x
)
&
−
0
-0
−
0
.
25
25
25
&
−
0
-0
−
0
.
74
74
74
&
−
0
-0
−
0
.
98
98
98
&
−
1
-1
−
1
.
0
0
0
\newline
\end{tabular}
\newline
What is a reasonable estimate for
lim
x
→
−
6
h
(
x
)
\lim _{x \rightarrow-6} h(x)
lim
x
→
−
6
h
(
x
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
-6
−
6
\newline
(B)
−
2
-2
−
2
\newline
(C)
−
1
-1
−
1
\newline
(D) The limit doesn't exist
Get tutor help
y
=
4.5
x
+
3
y
=
C
(
x
+
2
)
\begin{array}{l} y=4.5 x+3 \\ y=C(x+2) \end{array}
y
=
4.5
x
+
3
y
=
C
(
x
+
2
)
\newline
In the system of equations,
C
C
C
is a constant. For which values of
C
C
C
does the system have no solution?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
.
5
5
5
\newline
(B)
4
4
4
.
5
5
5
\newline
(C) All real numbers
\newline
(D) No 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
{
y
∣
y
≥
2
}
\left\{y \mid y \geq 2\right\}
{
y
∣
y
≥
2
}
\newline
{
y
∣
y
≤
0
}
\left\{y \mid y \leq 0\right\}
{
y
∣
y
≤
0
}
\newline
{
y
∣
y
≥
0
}
\left\{y \mid y \geq 0\right\}
{
y
∣
y
≥
0
}
\newline
all real numbers
\text{all real numbers}
all real numbers
Get tutor help
Previous
1
2
3
