59 / 84
©Sylvia S. Mader
LESSON 5
Graphing Cube Root Functions
1
Graph Cube Root Functions
A radical function that contains the cube root of a
variable is called a
cube root function.
The domain and range of a cube root function
are both all real numbers, and the graph of a cube root function has an
inflection point
, a
point on the curve where the curvature changes direction.
Key Concept
Parent Function of Cube Root Functions
Parent function:
Domain:
Range:
Intercepts:
Symmetry:
End behavior:
Extrema
Inflection point
f
(
x
)
=
3
√
x
{
x
| -∞<
x
< +∞
} or (
-∞
,
+∞
)
{
f
(
x
)
| –∞<
f
(
x
)
< +∞
} or (
-∞
,
+∞
)
x
=
0,
y
=
0
Point symmetry about the origin
f
(
x
)
→+∞
as
x
→+∞
,
f
(
x
)
→-∞
as
x
→-∞
None
(0, 0)
Identify the domain and range of
f
(
x
)
=
-
3
√
x
-
2. Describe the attributes of the graph.
Domain and Range
Domain: all numbers for which the
radicand is defined, all real numbers
D
=
{
x
| -∞ <
x
< +∞
} or (
–∞
,
+∞
)
Range: all output values for the
function, all real numbers
R = {
f
(
x
)
| -∞ <
f
(
x
)
< +∞
} or
(
-∞
,
+∞
)
Attributes
End behavior: The values
of
y
decrease as the
values of
x
increase.
f
(
x
)
→
-∞
as
x
→
+∞
f
(
x
)
→
+∞
as
x
→
-∞
Inflection point: (2, 0)
Guided Practice
1.
f
(
x
)
= -
3
√
x
+
3
Example 1
Identify Attributes of Cube Root Functions
Why?
A giraffe is a mammal that has an
average life span of 25 years in the
wild. It can range in height from 4 to
6 meters, and in weight from 794 to
1270 kilograms.
The height
h
in meters of some small
giraffes weighing
x
kilograms can be
approximated by the cube root
function
h
(
x
)
=
0.45
3
√
x
.
Now
1
Graph cube root
functions.
2
Analyze cube root
functions.
Then
You graphed square
root functions.
New
Vocabulary
cube root function
inflection point
Mathematical
Practices
1
Make sense of
problems.
2
Reason abstractly and
quantitatively.
4
Model with
mathematics.
7
Make use of structure.
C05_017A_903990
y
x
O
C05_018A_903990
y
x
O
C05_019A_903990
y
xO
connectED.mcgraw-hill.com345