Holt CA Course Cubic Functions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course Cubic Functions Warm Up Graph each function. 1. y = 2x y = –x – 1 3. y = x 2 – 4 4. y = x

Holt CA Course Cubic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards

Holt CA Course Cubic Functions Vocabulary cubic function

Holt CA Course 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.

Holt CA Course 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 – –2 – A. y = x x y –2 2 2 – (-2) (-1) (0) (1) (2)

Holt CA Course 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 – –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

Holt CA Course 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 – –7 B. y = –x –(–2) –(–1) –(0) –(1) –(2) 3 + 1

Holt CA Course Cubic Functions Create a table for each cubic function, and use it to graph the function. Check It Out! Example 1 A. y = x x x y –2 – x y –2 2 2 – (-2) (-1) (0) (1) (2)

Holt CA Course 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 – –2 –9 B. y = –x 3 – 1 –(–2) 3 – 1 –(–1) 3 – 1 –(0) 3 – 1 –(1) 3 – 1 –(2) 3 – 1

Holt CA Course 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 – – C. y = x (–2) (–1) (0) (1) (2) 3 + 2

Holt CA Course 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 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 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 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 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 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 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 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 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 –

Holt CA Course Cubic Functions Lesson Quiz: Part Il Tell whether each function is linear, quadratic, or cubic quadratic cubic linear