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Math Problems
Algebra 1
Domain and range of quadratic functions: equations
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
A cubic function is graphed in the
x
y
x y
x
y
-plane. Which of the following equations could represent the graph?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
x
(
x
−
1
)
(
x
+
2
)
y=x(x-1)(x+2)
y
=
x
(
x
−
1
)
(
x
+
2
)
\newline
(B)
y
=
x
(
x
+
1
)
(
x
−
2
)
y=x(x+1)(x-2)
y
=
x
(
x
+
1
)
(
x
−
2
)
\newline
(C)
y
=
−
x
(
x
−
1
)
(
x
+
2
)
y=-x(x-1)(x+2)
y
=
−
x
(
x
−
1
)
(
x
+
2
)
\newline
(D)
y
=
−
x
(
x
+
1
)
(
x
−
2
)
y=-x(x+1)(x-2)
y
=
−
x
(
x
+
1
)
(
x
−
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
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
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