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Mathematics
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College Algebra
Quiz 2: Functions and Relations
Path 4
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Question 241
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of y = f (3x) is the graph of y = f (x) with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).
Question 242
Multiple Choice
Solve the problem. -The table below shows the wind speed y (in mph) of a hurricane versus the barometric pressure x (in mb) .
Barometric
Pressure (mb) (x)
Wind
Speed (mph)
(
y
)
1
,
005
35
1
,
004
45
1
,
000
50
996
65
984
80
970
100
949
110
929
145
904
160
\begin{array}{|c|c|}\hline \begin{array}{c}\text { Barometric } \\\text { Pressure (mb) (x) }\end{array} & \begin{array}{c}\text { Wind } \\\text { Speed (mph) }(\mathbf{y}) \end{array} \\\hline 1,005 & 35 \\\hline 1,004 & 45 \\\hline 1,000 & 50 \\\hline 996 & 65 \\\hline 984 & 80 \\\hline 970 & 100 \\\hline 949 & 110 \\\hline 929 & 145 \\\hline 904 & 160 \\\hline\end{array}
Barometric
Pressure (mb) (x)
1
,
005
1
,
004
1
,
000
996
984
970
949
929
904
Wind
Speed (mph)
(
y
)
35
45
50
65
80
100
110
145
160
a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the
y
y
y
-intercept to the nearest whole unit. b. Use the model in part (a) to approximate the wind speed of a hurricane with a barometric pressure of
900
m
b
900 \mathrm { mb }
900
mb
.
Question 243
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -
The graph of
y
=
1
3
f
(
x
)
is the graph of
y
=
f
(
x
)
with a (choose one: vertical stretch, vertical shrink,
\text { The graph of } y = \frac { 1 } { 3 } f ( x ) \text { is the graph of } y = f ( x ) \text { with a (choose one: vertical stretch, vertical shrink, }
The graph of
y
=
3
1
f
(
x
)
is the graph of
y
=
f
(
x
)
with a (choose one: vertical stretch, vertical shrink,
horizontal stretch, horizontal shrink).
Question 244
Multiple Choice
Choose the one alternative that best completes the statement or answers the question. From memory match each equation with its graph. -
f
(
x
)
=
x
g
(
x
)
=
1
x
h
(
x
)
=
x
2
f(x) =\sqrt{x} \quad g(x) =\frac{1}{x} \quad h(x) =x^{2}
f
(
x
)
=
x
g
(
x
)
=
x
1
h
(
x
)
=
x
2
I
II
III
Question 245
Multiple Choice
Sketch the graph using transformations of a parent function (without a table of values) . -
h
(
x
)
=
x
−
2
3
h ( x ) = \sqrt [ 3 ] { x - 2 }
h
(
x
)
=
3
x
−
2
Question 246
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x) + c is the graph of y = f (x) shifted (up/down/left/right) c units.
Question 247
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of
y
=
−
f
(
x
)
y = - f ( x )
y
=
−
f
(
x
)
is the graph of
y
=
f
(
x
)
y = f ( x )
y
=
f
(
x
)
reflected across the ـــــــــــــaxis.
Question 248
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x + c) is the graph of y = f (x) shifted (up/down/left/right) c units.
Question 249
Multiple Choice
Sketch the graph using transformations of a parent function (without a table of values) . -
a
(
x
)
=
x
2
−
3
a ( x ) = x ^ { 2 } - 3
a
(
x
)
=
x
2
−
3
Question 250
Multiple Choice
Use translations to graph the given function. -
f
(
x
)
=
∣
x
+
1
∣
f ( x ) = | x + 1 |
f
(
x
)
=
∣
x
+
1∣
Question 251
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of
y
=
f
(
1
3
x
)
y = f \left( \frac { 1 } { 3 } x \right)
y
=
f
(
3
1
x
)
is the graph of
y
=
f
(
x
)
y = f ( x )
y
=
f
(
x
)
with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).
Question 252
Multiple Choice
Choose the one alternative that best completes the statement or answers the question. From memory match each equation with its graph. -
f
(
x
)
=
x
3
g
(
x
)
=
x
2
h
(
x
)
=
∣
x
∣
f(x) =\sqrt[3]{x} \quad g(x) =x^{2} \quad h(x) =|x|
f
(
x
)
=
3
x
g
(
x
)
=
x
2
h
(
x
)
=
∣
x
∣
I
II
III
Question 253
Short Answer
Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A function defined by f (x) = mx + b is a function and its graph is a line in a rectangular coordinate system.