1. Standards California AF3.1 Graph functions of the form
y = nx2 and y = nx3 and use in solving problems.
California
Standards

2. 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.

3. Additional Example 1: Graphing Cubic Functions
Create a table for each cubic function, and use it to graph the function. 1 4
A. y = x3 x y –2 2 –4 4 1 4 x x3 y –2 –1 1 2
(-2)3 1 4 –2
(-1)3 1 4
–0.25
(0)3 1 4
(1)3 1 4
0.25
(2)3 1 4 2

4. Additional Example 1: Graphing Cubic Functions
Create a table for each cubic function, and use it to graph the function.
B. y = –x3 + 1 x
–x3 + 1 y –2 –1 1 2
–(–2)3 + 1 9
–(–1)3 + 1 2
–(0)3 + 1 1
–(1)3 + 1
–(2)3 + 1 –7

5. Additional Example 1: Graphing Cubic Functions
Create a table for each cubic function, and use it to graph the function.
C. y = x3 – 2 x
x3 – 2 y –2 –1 1 2
(–2)3 – 2
–10
(–1)3 – 2 –3
(0)3 – 2 –2
(1)3 – 2 –1
(2)3 – 2 6

6. Check It Out! Example 1
Create a table for each cubic function, and use it to graph the function. 1 4
A. y = x3 + 1 x y –2 2 –4 4 1 4 x
x3 + 1 y –2 –1 1 2
(-2)3 + 1 1 4 –1
(-1)3 + 1 1 4
0.75
(0)3 + 1 1 4 1
(1)3 + 1 1 4
1.25
(2)3 + 1 1 4 3

7. Check It Out! Example 1 x –x3 – 1 y
Create a table for each cubic function, and use it to graph the function.
B. y = –x3 – 1 x
–x3 – 1 y –2 –1 1 2
–(–2)3 – 1 7
–(–1)3 – 1
–(0)3 – 1 –1
–(1)3 – 1 –2
–(2)3 – 1 –9

8. Check It Out! Example 1 x x3 + 2 y
Create a table for each cubic function, and use it to graph the function.
C. y = x3 + 2 x
x3 + 2 y –2 –1 1 2
(–2)3 + 2 –6
(–1)3 + 2 1
(0)3 + 2 2
(1)3 + 2 3
(2)3 + 2 10

9. Additional Example 2: Identifying Types of Functions
Tell whether the function is linear, quadratic, or cubic. A.
The graph is a parabola.
Quadratic

10. Additional Example 2: Identifying Types of Functions
Tell whether the function is linear, quadratic, or cubic. B.
The graph curves down, then up.
Cubic

11. Additional Example 2: Identifying Types of Functions
Tell whether the function is linear, quadratic, or cubic. C.
The graph is a parabola.
Quadratic

12. Additional Example 2: Identifying Types of Functions
Tell whether the function is linear, quadratic, or cubic. D.
The graph is a line.
Linear

13. Check It Out! Example 2 The graph is a parabola. Quadratic
Tell whether the function is linear, quadratic, or cubic. A.
The graph is a parabola.
Quadratic

14. Check It Out! Example 2 The graph is a line. Linear
Tell whether the function is linear, quadratic, or cubic. B.
The graph is a line.
Linear

15. The graph curves down, then up.
Check It Out! Example 2
Tell whether the function is linear, quadratic, or cubic. C.
The graph curves down, then up.
Cubic

16. Check It Out! Example 2 The graph is a parabola. Quadratic
Tell whether the function is linear, quadratic, or cubic. D.
The graph is a parabola.
Quadratic