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EXTEND 5
Graphing Technology Lab
Graphing
n
th Root Functions
In general, the graph of a cube root function is an
s-shaped curve. The graphs are not symmetric
with the
x
- or
y
-axis or the line
y
= -
x
there are
no asymptotes. The parent function (
x
)
=
3
x
can
be transformed using by
af
(
x
),
f
(
x
)
+
d
,
f
(
bx
), and
f
(
x
-
c
) for positive and negative values of
a
,
b
,
c
, and
d
.
Work cooperatively. Graph the set of functions on the same screen.
Describe any similarities and differences among the graphs.
f
(
x
)
=
3
√
x
,
g
(
x
)
=
2
3
x
,
h
(
x
)
=
3
2
x
,
j
(
x
)
= -
2
3
x
,
k
(
x
)
=
3
-
2
x
The graphs have the same general shape. The functions
f
(
x
),
g
(
x
), and
h
(
x
) lie in the first and third quadrants. The graphs
j
(
x
) and
k
(
x
) are
reflections and lie in the second and fourth quadrants. The graphs of
g
(
x
) and
j
(
x
) are more vertically stretched than
f
(
x
). The graphs of
h
(
x
)
and
k
(
x
) are more horizontally compressed than
f
(
x
) but less than
g
(
x
)
and
j
(
x
).
C06_011A_139256
[ 10, 10] scl: 1 by [ 10, 10] scl: 1
f
(
x
)
h
(
x
)
k
(
x
)
g
(
x
)
j
(
x
)
Activity 1
af
(
x
),
-
af
(
x
),
f
(
bx
), and
f
(
-
bx
)
Some transformations cause the graph of a function to change location but do not change
the shape from the parent function.
Work cooperatively. Graph the set of functions on the same screen.
Describe any similarities and differences among the graphs.
f
(
x
)
=
3
x
,
g
(
x
)
=
3
x
+
2,
h
(
x
)
=
3
x
-
2,
j
(
x
)
=
3
x
+
2,
k
(
x
)
=
3
x
-
2
The graphs have the same shape, but have been translated.
The graph of
g
(
x
) is shifted 2 units left and
h
(
x
) is shifted
2 units right while the graph of
j
(
x
) is shifted 2 units up and
k
(
x
) shifted 2 units down.
C06_012A_139256
[ 10, 10] scl: 2 by [ 5, 5] scl: 1
g
(
x
)
j
(
x
)
f
(
x
)
h
(
x
)
k
(
x
)
Activity 2
f
(
x
-
c
),
f
(
x
+
c
),
f
(
x
)
+
d
, and
f
(
x
)
-
d
Exercises
Work cooperatively. Examine each set of functions and predict the similarities and differences in their
graphs. Use a graphing calculator to confirm your prediction. Write a sentence or two comparing the
graphs.
1.
f
(
x
)
=
3
x
,
g
(
x
)
=
3
3
x
,
h
(
x
)
= -
3
3
x
2.
f
(
x
)
=
3
x
,
g
(
x
)
=
3
x
+
1,
h
(
x
)
=
3
x
-
1
3.
f
(
x
)
=
3
x
,
g
(
x
)
=
3
8
x
,
h
(
x
)
=
3
-
8
x
4.
f
(
x
)
=
3
x
,
g
(
x
)
=
3
x
-
8,
h
(
x
)
=
3
x
+
8
Mathematical Practices
4
Model with Mathematics
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