Download Answers for the lesson “Graph Square Root and Cube Root Functions”

Answers for the lesson “Graph Square Root
and Cube Root Functions”
LESSON
3.5
Skill Practice
y
6.
1. radical
2
21
x
2. a. The graph will be reflected
over the x-axis and will
rise faster.
b. The graph will be translated
2 units right.
c. The graph will be translated
domain: xq0, range: ya0
4 units up.
1
21
y
7.
y
3.
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
21
domain: xq0, range: ya0
4.
f(x)
x
domain: xq0, range: yq0
g(x)
8.
1
21
x
domain: xq0, range: f(x) q0
5.
21
y
1
21
3
x
domain: xq0, range: g(x)q0
x
9. D
domain: xq0, range: ya0
Algebra 2
Answer Transparencies for Checking Homework
104
10.
y
13.
y
1
4
0.2
22
x
22
x
domain: all real numbers,
range: all real numbers
y
11.
domain: all real numbers,
range: all real numbers
1
y
14.
22
x
3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
22
x
domain: all real numbers,
range: all real numbers
y
12.
domain: all real numbers,
range: all real numbers
2
22
15.
y
x
1
22
domain: all real numbers,
range: all real numbers
x
domain: all real numbers,
range: all real numbers
Algebra 2
Answer Transparencies for Checking Homework
105
16.
y
19.
y
1
22
x
domain: all real numbers,
range: all real numbers
1
21
x
y
20.
domain: xq1, range: yq3
y
17.
1
2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
21
22
x
domain: all real numbers,
range: all real numbers
domain: xq21, range: yq8
y
18.
domain: xq5, range: ya1
y
21.
1
21
x
x
2
22
x
domain: all real numbers,
range: all real numbers
Algebra 2
Answer Transparencies for Checking Homework
106
22.
25. The domain is limited because the
y
2
22
x
square root of a negative number
is not a real number. The range is
limited because the square root of
a number is nonnegative.
26. The graph was translated
domain: xq4, range: ya27
23.
y
1
22
x
horizontally in the wrong
direction; the graph of
3}
y 5 22Ïx 1 1 2 3 is the
3}
graph of y 5 22Ï x translated
left 1 unit and down 3 units.
27. C
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28. Domain: xq25, range yq0; the
expression under the radical sign
must be greater than or equal to 0,
so substitute the least value of x
into the equation and find y.
domain: all real numbers,
range: all real numbers
24.
y
29. Domain: xq12, range: yq0; the
expression under the radical sign
must be greater than or equal to 0,
so substitute the least value of x
into the equation and find y.
30. Domain: xq0, range: yq24; the
2
21
x
domain: all real numbers,
range: all real numbers
expression under the radical sign
must be greater than or equal to 0,
so substitute the least value of x
into the equation and find y.
31. Domain: all real numbers,
range: all real numbers; there are
no restrictions on finding the cube
root of a number and therefore no
restrictions on the range.
Algebra 2
Answer Transparencies for Checking Homework
107
Î
}
32. Domain: all real numbers, range:
all real numbers; there are no
restrictions on finding the cube
root of a number and therefore no
restrictions on the range.
165
39. a. vt 5 33.7 }
A
b. Sample:
A
vt 306.1
33. Domain: xq3, range: yq6; the
expression under the radical sign
must be greater than or equal to 0,
so substitute the least value of x
into the equation and find y.
34. Sample answer: If n is even, the
graph will have a restricted
domain and range. If n is odd,
the domain and range will be all
real numbers.
2
A
8
4
6
216.44
176.72
10
vt 153.05
136.89
c.
Vt
500
400
300
200
35. about 43 ft above sea level
36. a. about 1.6 sec
b. about 3.25 ft
Î
}
C
37. a. v 5 331.5 1 1 }
273.15
b. domain: Cq2273.15,
range: vq0
38. about 2470 horsepower
Speed (mi/h)
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Problem Solving
s
250
200
150
100
50
0
0
1000 2000 3000 p
Power (horsepower)
100
0
0
2
4
6
8
10 A
S
40. a. S 5 :r 2 1 :r, }F
5 r 2 1 r,
:
1
1
S
4
4
:
1
1 2
S
}5 r1} ,
}F
1
4
2
:
}
1
1
S
} 5 r 1 },
}F
1
4
2
:
}
1
4S 1 :
}
F 5 r 1 },
2
4:
}
1
:
1
}
} S 1 } 5 r 1 },
2
4
Ï :F
}
1
:
1
}
} S 1 } 2 } 5 r
2
4
Ï :F
}F
1 } 5 r 2 1 r 1 },
Î
Î
1
2
Î
Î
Algebra 2
Answer Transparencies for Checking Homework
108
40. b.
r
2
1.5
1
0.5
0
2
4
6
8
S
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
0
Algebra 2
Answer Transparencies for Checking Homework
109