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Math Problems
Precalculus
Transformations of functions
f
(
x
)
=
10
(
1.25
)
x
f(x)=10(1.25)^{x}
f
(
x
)
=
10
(
1.25
)
x
\newline
The function models
f
f
f
, the price of a rare trading card in dollars
x
x
x
years after its initial release in
1993
1993
1993
. Based on the model, what is the price of the trading card
20
20
20
years after its initial release?
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What is the value of
𝑥
𝑥
x
in the solution to the system of equations?
\newline
2
x
+
2
y
=
11
2x+2y=11
2
x
+
2
y
=
11
\newline
4
x
−
y
=
28
4x-y=28
4
x
−
y
=
28
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Write the equation for
g
g
g
that represents the indicated transformation of the graph
f
f
f
.
f
(
x
)
=
log
x
f(x)=\log x
f
(
x
)
=
lo
g
x
; translation
3
3
3
units to the left and
2
2
2
units up, followed by a reflection in the
x
\mathrm{x}
x
axis
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The length of a rectangle's diagonal is
2
29
2 \sqrt{29}
2
29
, and the length of the longer side is
10
10
10
. What is the area of the rectangle?
\newline
A)
116
116
116
\newline
B)
20
29
20 \sqrt{29}
20
29
\newline
C)
10
29
10 \sqrt{29}
10
29
\newline
D)
40
40
40
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evaluate
8
−
m
n
+
p
2
8-\frac{m}{n}+p^2
8
−
n
m
+
p
2
when
m
=
8
m=8
m
=
8
,
n
=
2
n=2
n
=
2
,
p
=
7
p=7
p
=
7
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Which of the following is a correct interpretation of the expression
−
2
−
7
-2-7
−
2
−
7
?
\newline
Choose
1
1
1
answer:
\newline
(A) Start at
−
2
-2
−
2
on the number line and move
7
7
7
to the left.
\newline
(B) Start at
−
2
-2
−
2
on the number line and move
7
7
7
to the right.
\newline
(C) Start at
7
7
7
on the number line and move
2
2
2
to the left.
\newline
(D) Start at
7
7
7
on the number line and move
2
2
2
to the right.
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If
153
=
2
(
z
+
z
)
n
153=2(z+z)n
153
=
2
(
z
+
z
)
n
, then what is the value of
2
n
(
2
z
)
−
193
2n(2z)-193
2
n
(
2
z
)
−
193
?
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is scaled vertically by a factor of
2
3
\frac{2}{3}
3
2
.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is reflected across the
x
x
x
-axis and then scaled vertically by a factor of
5
5
5
.
\newline
What is the equation of the new parabola?
\newline
y
=
□
y=\square
y
=
□
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is scaled vertically by a factor of
1
10
\frac{1}{10}
10
1
.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is shifted up by
7
7
7
units and to the left by
1
1
1
unit.
\newline
What is the equation of the new parabola?
\newline
y
=
□
y=\square
y
=
□
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is shifted up by
4
4
4
units.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is shifted down by
3
3
3
units and to the left by
2
2
2
units.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is scaled vertically by a factor of
7
7
7
. What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is shifted down by
6
6
6
units and to the right by
5
5
5
units.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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The parabola
y
=
x
2
y=x^{2}
y
=
x
2
is shifted up by
2
2
2
units and to the right by
3
3
3
units.
\newline
What is the equation of the new parabola?
\newline
y
=
y=
y
=
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