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Math Problems
Algebra 1
Domain and range of quadratic functions: equations
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
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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
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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?
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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
?
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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
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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
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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
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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
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