1. Holt CA Course 1 7-5 Cubic Functions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 7-5 Cubic Functions Warm Up Graph each function. 1. y = 2x + 4 2. y = –x – 1 3. y = x 2 – 4 4. y = x 2 1212

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

4. Holt CA Course 1 7-5 Cubic Functions Vocabulary cubic function

5. 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 = nx 3 where n ≠ 0.

6. 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 x 3 y –2 –1 0 1 2 –2 –0.25 0 0.25 2 A. y = x 3 1414 x y –2 2 2 –4 4 4 1414 (-2) 3 1414 (-1) 3 1414 (0) 3 1414 (1) 3 1414 (2) 3 1414

7. 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 xx 3 – 2y –2 –1 0 1 2 –10 –3 –2 –1 6 C. y = x 3 – 2 (–2) 3 – 2 (–1) 3 – 2 (0) 3 – 2 (1) 3 – 2 (2) 3 – 2

8. 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–x 3 + 1y –2 –1 0 1 2 9 2 1 0 –7 B. y = –x 3 + 1 –(–2) 3 + 1 –(–1) 3 + 1 –(0) 3 + 1 –(1) 3 + 1 –(2) 3 + 1

9. 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 = x 3 + 1 1414 x x 3 + 1 y –2 –1 0 1 2 0.75 1 1.25 3 x y –2 2 2 –4 4 4 1414 (-2) 3 + 1 1414 (-1) 3 + 1 1414 (0) 3 + 1 1414 (1) 3 + 1 1414 (2) 3 + 1 1414

10. 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–x 3 – 1y –2 –1 0 1 2 7 0 –2 –9 B. y = –x 3 – 1 –(–2) 3 – 1 –(–1) 3 – 1 –(0) 3 – 1 –(1) 3 – 1 –(2) 3 – 1

11. 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 xx 3 + 2y –2 –1 0 1 2 –6 1 2 3 10 C. y = x 3 + 2 (–2) 3 + 2 (–1) 3 + 2 (0) 3 + 2 (1) 3 + 2 (2) 3 + 2

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. Holt CA Course 1 7-5 Cubic Functions Lesson Quiz: Part I Create a table for each cubic function, and use it to graph the function. 1. y = – x 3 2. y = x 3 – 3 1212

21. Holt CA Course 1 7-5 Cubic Functions Lesson Quiz: Part Il Tell whether each function is linear, quadratic, or cubic. 3. 4. 5. quadratic cubic linear