Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use...
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Transcript of Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use...
![Page 1: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/1.jpg)
Holt CA Course 1
7-5 Cubic Functions
AF3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
California Standards
![Page 2: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/2.jpg)
Holt CA Course 1
7-5 Cubic Functions
A cubic function is a function in which the greatest power of the variable is 3. The most basic cubic function is y = nx3 where n ≠ 0.
![Page 3: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/3.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Additional Example 1: Graphing Cubic Functions
x x3 y
–2
–1
0
1
2
–2
–0.25
0
0.25
2
A. y = x314
x
y
–2
–2
2
2–4
–4
4
414
(-2)314
(-1)314
(0)314
(1)314
(2)314
![Page 4: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/4.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Additional Example 1: Graphing Cubic Functions
x –x3 + 1 y
–2
–1
0
1
2
9
2
1
0
–7
B. y = –x3 + 1
–(–2)3 + 1
–(–1)3 + 1
–(0)3 + 1
–(1)3 + 1
–(2)3 + 1
![Page 5: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/5.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Additional Example 1: Graphing Cubic Functions
x x3 – 2 y
–2
–1
0
1
2
–10
–3
–2
–1
6
C. y = x3 – 2
(–2)3 – 2
(–1)3 – 2
(0)3 – 2
(1)3 – 2
(2)3 – 2
![Page 6: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/6.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Check It Out! Example 1
A. y = x3 + 114
x x3 + 1 y
–2
–1
0
1
2
–1
0.75
1
1.25
3
x
y
–2
–2
2
2–4
–4
4
414
(-2)3 + 114
(-1)3 + 114
(0)3 + 114
(1)3 + 114
(2)3 + 114
![Page 7: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/7.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Check It Out! Example 1
x –x3 – 1 y
–2
–1
0
1
2
7
0
–1
–2
–9
B. y = –x3 – 1
–(–2)3 – 1
–(–1)3 – 1
–(0)3 – 1
–(1)3 – 1
–(2)3 – 1
![Page 8: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/8.jpg)
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function.
Check It Out! Example 1
x x3 + 2 y
–2
–1
0
1
2
–6
1
2
3
10
C. y = x3 + 2
(–2)3 + 2
(–1)3 + 2
(0)3 + 2
(1)3 + 2
(2)3 + 2
![Page 9: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/9.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
A.
Additional Example 2: Identifying Types of Functions
The graph is a parabola.Quadratic
![Page 10: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/10.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
B.
Additional Example 2: Identifying Types of Functions
The graph curves down, then up.
Cubic
![Page 11: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/11.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
C.
Additional Example 2: Identifying Types of Functions
The graph is a parabola.
Quadratic
![Page 12: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/12.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
D.
Additional Example 2: Identifying Types of Functions
The graph is a line.
Linear
![Page 13: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/13.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
A.
Check It Out! Example 2
The graph is a parabola.
Quadratic
![Page 14: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/14.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
B.
Check It Out! Example 2
The graph is a line.
Linear
![Page 15: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/15.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
C.
Check It Out! Example 2
The graph curves down, then up.
Cubic
![Page 16: Holt CA Course 1 7-5 Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards.](https://reader035.fdocuments.us/reader035/viewer/2022070414/5697c0221a28abf838cd3a3d/html5/thumbnails/16.jpg)
Holt CA Course 1
7-5 Cubic Functions
Tell whether the function is linear, quadratic, or cubic.
D.
Check It Out! Example 2
The graph is a parabola.
Quadratic