Section 9.1
The Square Root Function
879
Version: Fall 2007
9.1
Exercises
In
Exercises 1

10
, complete each of the
following tasks.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
ii.
Complete the table of points for the
given function. Plot each of the points
on your coordinate system, then use
them to help draw the graph of the
given function.
iii. Use di
ff
erent colored pencils to project
all points onto the
x
 and
y
axes to
determine the domain and range. Use
interval notation to describe the do
main of the given function.
1.
f
(
x
) =

√
x
x
0
1
4
9
f
(
x
)
2.
f
(
x
) =
√

x
x
0

1

4

9
f
(
x
)
3.
f
(
x
) =
√
x
+ 2
x

2

1
2
7
f
(
x
)
4.
f
(
x
) =
√
5

x
x

4
1
4
5
f
(
x
)
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1
5.
f
(
x
) =
√
x
+ 2
x
0
1
4
9
f
(
x
)
6.
f
(
x
) =
√
x

1
x
0
1
4
9
f
(
x
)
7.
f
(
x
) =
√
x
+ 3 + 2
x

3

2
1
6
f
(
x
)
8.
f
(
x
) =
√
x

1 + 3
x
1
2
5
10
f
(
x
)
9.
f
(
x
) =
√
3

x
x

6

1
2
3
f
(
x
)
10.
f
(
x
) =

√
x
+ 3
x

3

2
1
6
f
(
x
)
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880
Chapter 9
Radical Functions
Version: Fall 2007
In
Exercises 11

20
, perform each of the
following tasks.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
Remember to draw all lines with
a ruler.
ii.
Use geometric transformations to draw
the graph of the given function on
your coordinate system without the
use of a graphing calculator.
Note:
You may
check
your solution with
your calculator, but you should be
able to produce the graph without
the use of your calculator.
iii. Use di
ff
erent colored pencils to project
the points on the graph of the func
tion onto the
x
 and
y
axes. Use in
terval notation to describe the domain
and range of the function.
11.
f
(
x
) =
√
x
+ 3
12.
f
(
x
) =
√
x
+ 3
13.
f
(
x
) =
√
x

2
14.
f
(
x
) =
√
x

2
15.
f
(
x
) =
√
x
+ 5 + 1
16.
f
(
x
) =
√
x

2

1
17.
f
(
x
) =

√
x
+ 4
18.
f
(
x
) =

√
x
+ 4
19.
f
(
x
) =

√
x
+ 3
20.
f
(
x
) =

√
x
+ 3
21.
To draw the graph of the function
f
(
x
) =
√
3

x
, perform each of the fol
lowing steps in sequence without the aid
of a calculator.
i.
Set up a coordinate system and sketch
the graph of
y
=
√
x
. Label the graph
with its equation.
ii.
Set up a second coordinate system
and sketch the graph of
y
=
√

x
.
Label the graph with its equation.
iii. Set up a third coordinate system and
sketch the graph of
y
=

(
x

3)
.
Label the graph with its equation. This
is the graph of
f
(
x
) =
√
3

x
. Use
interval notation to state the domain
and range of this function.
22.
To draw the graph of the function
f
(
x
) =
√

x

3
, perform each of the
following steps in sequence.
i.
Set up a coordinate system and sketch
the graph of
y
=
√
x
. Label the graph
with its equation.
ii.
Set up a second coordinate system
and sketch the graph of
y
=
√

x
.
Label the graph with its equation.
iii. Set up a third coordinate system and
sketch the graph of
y
=

(
x
+ 3)
.
Label the graph with its equation. This
is the graph of
f
(
x
) =
√

x

3
. Use
interval notation to state the domain
and range of this function.
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 Pythagorean Theorem, Radical Functions

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