Name———————————————————————— Date —————————————
Practice A
Lesson
3.5
For use with the lesson “Graph Square Root and Cube Root Functions”
Match the function with its graph.
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3. f (x) 5 2​Ï x 1 1 ​ 
3}
6. f (x) 5 2​ Ï  x 1 1 ​ 
1. f(x) 5 ​Ï x ​ 1 1
2. f(x) 5 Ï
​ x 1 1 ​ 
3}
5. f(x) 5 Ï
​   x 2 1 ​ 
4. f(x) 5 Ï
​    x 1 1 ​ 
A.
y
B.
}
3}
y
C.
y
2
2
1
Lesson 3.5
1
D.
x
1
y
E.
1
x
y
F.
y
1
1
x
1
1
x
1
x
2
x
Graph the function. Then state the domain and range.
}
y
}
8. f(x) 5 Ï
​ x ​ 1 3
9. f (x) 5 ​Ï x 1 2 ​ 
y
y
1
1
1
x
1
1
1
}
3}
y
x
3}
12. f (x) 5 Ï
​   x 2 3 ​ 
11. f(x) 5 Ï
​    x ​ 1 2
10. f(x) 5 2​Ïx 2 3 ​ 
1
y
1
1
y
1
x
1
x
1
In Exercises 13 and 14, use the following information.
Falling Object A stone is dropped from a height of 150 feet. The time it takes for the stone to
1
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reach a height of h feet is given by the function t 5 ​ }4 ​ ​Ï150 2 h ​ 
where t is the time in seconds.
13. Identify the domain and range of the function.
14. What is the height of the stone after 2 seconds?
3-56
Algebra 2
Chapter Resource Book
x
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
}
7. f(x) 5 ​Ï x ​ 2 2
Lesson 3.5 Graph Square Root
and Cube Root Functions,
continued
7.
y
y
8.
y
1
1
x
1
y
x
1
1
1
x
domain: x ≥ 0, domain: x ≥ 0,
range: y ≥ 22 range: y ≥ 3
y
y
9.
10.
1
1
2
x
1
1
Investigating Algebra Activity
}
answers
6.
7.
x
x
1
}
1. a. y 5 Ï
​ x ​ 1 1 is y 5 Ï
​ x ​ shifted up 1 unit.
}
}
​ x ​ shifted down 2 units.
y 5 ​Ï x ​ 2 2 is y 5 Ï
}
}
is y 5 Ï
​ x ​ shifted to the left 3 units.
b. y 5 Ï
​ x 1 3 ​ 
}
}
is y 5 Ï
​ x ​ shifted to the right 5 units.
y5Ï
​ x 2 5 ​ 
}
1 }
c. y 5 }
​ 3 ​ ​Ï x ​ is a vertical shrink of y 5 Ï
​ x ​. 
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
}
1. E 2. A 3. D 4. C 5. F 6. B
2
1
}
y 5 22​Ï 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 ≥ 22, domain: x ≥ 3,
range: y ≥ 0 range: y ≤ 0
y
y
11.
12.
1
x
x
1
domain and range: domain and range:
all real numbers all real numbers
13. domain: 0 ≤ h ≤ 150, range: 0 ≤ t ≤ 3.06
14. 86 ft
Practice Level B
1.
y
2.
1
1
1
x
y
x
1
domain: x ≥ 0, range: y ≥ 22 3.
y
1
domain: x ≥ 2,
range: y ≥ 0
4.
y
1
1
x
domain: x ≥ 21, range: y ≥ 0 2
x
domain: x ≥ 22,
range: y ≥ 22
Algebra 2
Chapter Resource Book
A41