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Holt CA Course 1
7-5 Cubic Functions
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
7-5 Cubic Functions
Warm UpGraph each function.
1. y = 2x + 4
2. y = –x – 1
3. y = x2 – 4
4. y = x2 12
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
Holt CA Course 1
7-5 Cubic Functions
Vocabulary
cubic function
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.
Holt CA Course 1
7-5 Cubic Functions
Create a table for each cubic function, and use it to graph the function. (Use 5 ‘x’ values: +, 0, and -)
Notes 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
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
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
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
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
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
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
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
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
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
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
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
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
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
Holt CA Course 1
7-5 Cubic Functions
Lesson Quiz: Part ICreate a table for each cubic function, and use it to graph the function.
1. y = – x3
2. y = x3 – 3
1 2
Holt CA Course 1
7-5 Cubic Functions
Lesson Quiz: Part IlTell whether each function is linear, quadratic, or cubic.
3.
4.
5.
quadratic
cubic
linear
