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Math Problems
Algebra 2
Dilations of functions
Which function would be produced by a horizontal stretch of the graph of
\newline
y
=
x
y=\sqrt{x}
y
=
x
followed by a reflection in the
\newline
x
x
x
-axis?
\newline
y
=
2
(
−
x
)
y=\sqrt{2(-x)}
y
=
2
(
−
x
)
\newline
y
=
−
2
x
y=-\sqrt{2x}
y
=
−
2
x
\newline
y
=
(
1
2
)
(
−
x
)
y=\sqrt{\left(\frac{1}{2}\right)(-x)}
y
=
(
2
1
)
(
−
x
)
\newline
y
=
−
(
1
2
)
x
y=-\sqrt{\left(\frac{1}{2}\right)x}
y
=
−
(
2
1
)
x
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Use a standard enthulpies of formation table to determine the
Δ
H
f
\Delta H_f
Δ
H
f
for each of these renetlons. State whether each reaction is endothermic or exothermic. a)
2
CO
(
g
)
+
O
2
(
g
)
→
2
CO
2
(
g
)
2\text{CO}(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g)
2
CO
(
g
)
+
O
2
(
g
)
→
2
CO
2
(
g
)
b)
2
H
2
S
(
g
)
+
3
O
2
(
g
)
→
2
H
2
O
(
l
)
+
2
SO
2
(
g
)
2\text{H}_2\text{S}(g) + 3\text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) + 2\text{SO}_2(g)
2
H
2
S
(
g
)
+
3
O
2
(
g
)
→
2
H
2
O
(
l
)
+
2
SO
2
(
g
)
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The shapes drawn are similar. Figure
\newline
A is the original drawing and figure
\newline
B is the image.
\newline
(a) Does the original
\newline
(A) to the image
\newline
(B) represent an enlargement, a reduction, or are
\newline
A and
\newline
B congruent?
\newline
A
→
B
A \rightarrow B
A
→
B
\newline
Enlargement
\newline
A
→
B
A \rightarrow B
A
→
B
\newline
A
A
A
and
\newline
B
B
B
\newline
Reduction
\newline
Congruent
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The shapes drawn are similar. Figure
A
A
A
is the original drawing and figure
B
B
B
is the image.
\newline
Use the ruler to measure side lengths.
\newline
(a) Does the original (A) to the image (B) represent an enlargement, a reduction, or are
A
\mathrm{A}
A
and
B
\mathrm{B}
B
congruent?
\newline
A
→
B
A \rightarrow B
A
→
B
\newline
Enlargement
\newline
A
→
B
A \rightarrow B
A
→
B
\newline
Reduction
\newline
A
A
A
and
B
B
B
Congruent
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As the temperature of a chemical reaction in the gas phase is increased, the rate of the reaction increases because
\newline
(
1
1
1
) fewer particle collisions occur
\newline
(
2
2
2
) more effective particle collisions occur
\newline
(
3
3
3
) the required activation energy increases
\newline
(
4
4
4
) the concentration of the reactants increases
\newline
1
1
1
\newline
2
2
2
\newline
3
3
3
\newline
4
4
4
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what is the asymptote of the exponential function if the equation to the graph is
2
x
+
1
2^x + 1
2
x
+
1
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The graph of
y
=
8
(
0.5
)
x
3
y=8(0.5)^{\frac{x}{3}}
y
=
8
(
0.5
)
3
x
is shown in the
x
y
xy
x
y
-plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
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Evaluate the limit:
lim
x
→
1
x
−
1
1
−
x
\lim _{x \rightarrow 1} \frac{x-1}{1-\sqrt{x}}
lim
x
→
1
1
−
x
x
−
1
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If
y
=
1.
8
x
+
1
y=1.8^{x}+1
y
=
1.
8
x
+
1
is graphed in the
x
y
xy
x
y
-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
y
y
-intercept
\newline
(B)
x
x
x
-intercept
\newline
(C) Slope
\newline
(D) The value
y
y
y
approaches as
x
x
x
decreases
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What does the transformation
f
(
x
)
↦
f
(
4
x
)
f(x) \mapsto f(4x)
f
(
x
)
↦
f
(
4
x
)
do to the graph of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Choices:
\newline
[A] stretches it vertically
\newline
[B] stretches it horizontally
\newline
[C]shrinks it horizontally
\newline
[D]shrinks it vertically
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