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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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