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Section 2.6 Horizontal Geometric Transformations
209
Version: Fall 2007
2.6
Exercises
Pictured below is the graph of a function
f
.
x
10
y
10
f
The table that follows evaluates the
function
f
in the plot at key values of
x
.
Notice the horizontal format, where the
ﬁrst point in the table is the ordered pair
(
−
6
,
0).
x
−
6
−
4
−
2
0
2
4
f
(
x
)
0
4
4
0
−
2
0
Use the graph and the table to complete
each of following tasks for
Exercises 1

10
.
i. Set up a coordinate system on graph
paper. Label and scale each axis, then
copy and label the original graph of
f
onto your coordinate system.
Re
member to draw all lines with a ruler.
ii. Use the original table to help com
plete the table for the given function
in the exercise.
iii. Using a diﬀerent colored pencil, plot
the data from your completed table
on the
same
coordinate system as the
original graph of
f
. Use these points
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1
to help complete the graph of the given
function in the exercise, then label
this graph with its equation given in
the exercise.
1.
y
=
f
(2
x
).
x
−
3
−
2
−
1
0
1
2
y
2.
y
=
f
((1
/
2)
x
).
x
−
12
−
8
−
4
0
4
8
y
3.
y
=
f
(
−
x
).
x
−
4
−
2
0
2
4
6
y
4.
y
=
f
(
x
+ 3).
x
−
9
−
7
−
5
−
3
−
1
1
y
5.
y
=
f
(
x
−
1).
x
−
5
−
3
−
1
1
3
5
y
6.
y
=
f
(
−
2
x
).
x
−
2
−
1
0
1
2
3
y
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Chapter 2 Functions
Version: Fall 2007
7.
y
=
f
((
−
1
/
2)
x
).
x
−
8
−
4
0
4
8
12
y
8.
y
=
f
(
−
x
−
2).
x
−
6
−
4
−
2
0
2
4
y
9.
y
=
f
(
−
x
+ 1).
x
−
3
−
1
1
3
5
7
y
10.
y
=
f
(
−
x/
4).
x
−
16
−
8
0
8
16
24
y
11.
Use your graphing calculator to draw
the graph of
y
=
√
x
. Then, draw the
graph of
y
=
√
−
x
. In your own words,
explain what you learned from this exer
cise.
12.
Use your graphing calculator to draw
the graph of
y
=

x

. Then, draw the
graph of
y
=
 −
x

. In your own words,
explain what you learned from this exer
cise.
13.
Use your graphing calculator to draw
the graph of
y
=
x
2
. Then, in succession,
draw the graphs of
y
= (
x
−
2)
2
,
y
=
(
x
−
4)
2
, and
y
= (
x
−
6)
2
. In your own
words, explain what you learned from
this exercise.
14.
Use your graphing calculator to draw
the graph of
y
=
x
2
. Then, in succession,
draw the graphs of
y
= (
x
+ 2)
2
,
y
=
(
x
+ 4)
2
, and
y
= (
x
+ 6)
2
. In your own
words, explain what you learned from
this exercise.
15.
Use your graphing calculator to draw
the graph of
y
=

x

. Then, in succession,
draw the graphs of
y
=

2
x

,
y
=

3
x

,
and
y
=

4
x

. In your own words, explain
what you learned from this exercise.
16.
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