Download Graphing Cubic, Square Root and Cube Root Functions

GRAPHING CUBIC, SQUARE ROOT
AND CUBE ROOT FUNCTIONS
Focus 11 - Learning Goal: Students will be able to construct,
compare and analyze function models and interpret and
solve contextual problems.
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:
- Make connection
with other concepts
in math.
- Make connection
with other content
areas.
3
Students will be able to
construct, compare, and
analyze function models and
interpret and solve contextual
problems.
Function models:
- absolute value
- square root
- cube root
- piecewise
Analyze multiple
representations of functions
using:
- Key features
- Translations
- Parameters/limits of domain
2
Students will be able
to construct and
compare function
models and solve
contextual problems.
Function models:
- linear
- exponential
- quadratic
Illustrate the
graphical effects of
translations on
function models
using technology.
1
With help from the
teacher, the
student has partial
success with the
unit content.
0
Even with help,
the student has
no success with
the unit content.
Use your calculator to create a table of
values of the following equations.
 y = x2 and y = 𝒙
 What do you notice about the
values in the two y-columns?
 Why are all the y-values for
y = x2 positive?
 Why do all negative x-values
produce an error for y = 𝒙 ?
x
4
2
0
-2
-4
y = x2
x
y= 𝑥
16
4
0
4
4
2
2
1.41
0
Error
Error
16
0
-2
-4
y=
2
x
and y = 𝒙
 What is the domain of y = x2
and y = 𝒙 ?
 The domain of y = x2 is all real
numbers.
 The domain of y = 𝑥 is x ≥ 0.
 What is the range of y = x2 and
y= 𝒙?
 The range of y = x2 is y ≥ 0.
 The range of y = 𝑥 is y ≥ 0.
x
4
2
0
-2
-4
y = x2
x
y= 𝑥
16
4
0
4
4
2
2
1.41
0
Error
Error
16
0
-2
-4
Use the website www.desmos.com/calculator
2
to graph y = x and y = 𝒙
 What similarities and differences do
you see between these two graphs?
 Both graphs intersect at (0, 0) and
(1, 1)
 The square root function is a
reflection of the part of the
quadratic function in the first
quadrant, about y = x (when x is
positive).
 One opens up and one goes to the
right….
 Why do they intersect at (0, 0) and
(1, 1)?
y = x2
y= 𝒙
y=
3
x
𝟑
and y = 𝒙
 Make a prediction about the
relationship between y = x3 and y = 3 𝑥.
 Both functions will include all real
numbers in their domain and range
since a cubed number can be positive
and negative, as well as the cube root
of a number.
 Create data tables for y = x3 and
y = 𝟑 𝒙. (You may use your calculator.)
x
-8
-2
-1
0
1
2
8
y = x3
-512
-8
-1
0
3
x
y= 𝟑
-8
-2
-1
-2
-1.26
-1
0
1
1.26
2
1
8
0
1
2
512
8
Use the website www.desmos.com/calculator
𝟑
3
to graph y = x and y = 𝒙
 Use the “functions” button, select “misc”
to find the “cube root” button.
 What observations can you make about
the relationships between y = x3 and y =
𝟑
𝒙?
 The share the points (0, 0), (1, 1) and
(-1, -1).
 The domain and range of both functions
are all real numbers.
 They are both symmetric about the
origin.
y = x3
𝟑
y= 𝒙