Name ———————————————————————
LESSON
3.5
Date ————————————
Practice B
For use with the lesson “Graph Square Root and Cube Root Functions”
Graph the square root function. Then state the domain and range.
}
}
1. f(x) 5 Ï x 2 2
}
2. f (x) 5 Ï x 2 2
y
3. f (x) 5 3Ï x 1 1
y
1
y
1
1
x
1
}
x
1
}
4. f(x) 5 Ï x 1 2 2 2
}
6. f (x) 5 2Ï x 2 3
5. f (x) 5 Ï x 2 1 1 1
y
y
y
1
1
x
1
x
1
x
1
LESSON 3.5
1
x
1
Graph the cube root function. Then state the domain and range.
3}
3}
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
7. f(x) 5 Ï x 1 1
3}
8. f (x) 5 Ï x 2 4
y
9. f (x) 5 3Ï x
y
1
y
1
x
1
3}
1
x
1
3}
3}
11. f (x) 5 2Ï x 2 1
10. f(x) 5 Ï x 1 2
y
12. f (x) 5 Ï x 1 2 2 2
y
1
1
y
x
1
1
1 x
x
1
1
x
In Exercises 13 and 14, use the following information.
Speed of Sound The speed of sound in feet per second through air of any temperature
}
1087Ï t 1 273
measured in degrees Celsius is given by V 5 }}
where t is the temperature.
16.52
13. Identify the domain and range of the function.
14. What is the temperature of the air if the speed of sound is 1250 feet per second?
Algebra 2
Chapter Resource Book
3-57
Lesson 3.5 Graph Square Root
and Cube Root Functions,
continued
7.
8.
y
y
1
1
x
1
y
x
1
1
1
x
domain: x q 0,
range: y q 22
9.
1
1
x
x
x
1
}
}
}
c. y 5 } Ï x is a vertical shrink of y 5 Ï x .
}
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
y
1
1
1. a. y 5 Ï x 1 1 is y 5 Ï x shifted up 1 unit.
}
}
y 5 Ï x 2 2 is y 5 Ï x shifted down 2 units.
}
}
b. y 5 Ï x 1 3 is y 5 Ï x shifted to the left 3 units.
}
}
y 5 Ï x 2 5 is y 5 Ï x shifted to the right 5 units.
1
3
10.
y
2
Investigating Algebra Activity
}
domain: x q 0,
range: y q 3
ANSWERS
6.
y
7.
1. E 2. A 3. D 4. C 5. F 6. B
11.
domain: x q 3,
range: y a 0
12.
y
y
2
1
}
y 5 22Ï x is a vertical stretch of y 5 Ï x and
reflected in the x-axis.
2. They are the parent function with a vertical
translation. The parent function is translated up
when a number is added to the square root of x
and down when a number is subtracted from the
square root of x. 3. They are the parent function
with a horizontal translation. The parent function
is translated to the left when a number is added to
x before the square root is taken and to the right
when a number is subtracted from x before the
square root is taken.
4. They are the parent function with a vertical
shrink or stretch and a reflection. The parent
function is a vertical stretch when it is multiplied
by a number with an absolute value that is greater
than 1 and a vertical shrink when it is multiplied
by a number with an absolute value that is less
than 1. The parent function is reflected in the
x-axis when it is multiplied by a negative number.
5. For a square root function written in standard
form, a describes the vertical shrink or stretch of
the graph, h denotes the horizontal shift, and k
denotes the vertical shift of the parent function.
Practice Level A
domain: x q 22,
range: y q 0
1
x
x
1
domain and range:
domain and range:
all real numbers
all real numbers
13. domain: 0 a h a 150, range: 0 a t a 3.06
14. 86 ft
Practice Level B
1.
2.
y
1
1
1
x
x
1
domain: x q 0,
range: y q 22
3.
y
domain: x q 2,
range: y q 0
4.
y
1
y
1
1
x
domain: x q 21,
range: y q 0
2
x
domain: x q 22,
range: y q 22
Algebra 2
Chapter Resource Book
A41
5.
6.
y
1
3.
2
8.
6.
1 x
1
1
x
domain and range:
all real numbers
8.
y
3
y
domain and range:
all real numbers
1 x
9.
y
1
domain and range:
all real numbers
12.
y
1
13. domain: t q 2273,
domain and range:
all real numbers
23
10. (0, 0) and (1, 1) 11. On the interval 0 to 1,
12.
y
1
range: V q 0
1
x
about 87.98C
Practice Level C
1.
2.
y
13. (21, 21), (0, 0) and (1, 1) 14. On the
y
interval 21 to 1, the larger the root, the steeper the
graph. On the intervals 2` to 21 and 1 to `, the
larger the root, the less steep the graph.
1
1 x
15.
1
1
domain: x q 24,
range: y q 22
A42
; domain and range: all real
numbers
the larger the root, the steeper the graph. On the
interval 1 to `, the larger the root, the less steep
the graph.
domain and range:
all real numbers
14.
x
x
1
x
domain and range:
all real numbers
y
21
1
x
x
1
1
domain and range:
all real numbers
y
1
2
x
domain and range:
all real numbers
1
domain and range:
all real numbers
10.
y
x
domain and range:
all real numbers
x
1
7.
11.
y
1
1
1
domain: x q 22,
range: y a 2
y
y
1
9.
1
domain: x q 3,
range: y a 0
y
1
x
domain: xq 0,
range: y a 3
x
1
5.
7.
x
1
y
x
domain: x q 1,
range: y q 1
y
1
1
1
4.
y
Algebra 2
Chapter Resource Book
domain: x q 2,
range: y q 3
y
x
1
1
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ANSWERS
Lesson 3.5 Graph Square Root
and Cube Root Functions,
continued