Funciones pares e impares explicación gráfica

Takeaways

• 😀 Even functions are symmetric with respect to the y-axis. This means the graph mirrors itself across the y-axis.
• 😀 A function is even if f(-x) = f(x), which can be verified graphically or numerically.
• 😀 Example of an even function: f(x) = x². The graph of x² is symmetric around the y-axis.
• 😀 The concept of folding the graph along the y-axis helps visualize even symmetry.
• 😀 An odd function is symmetric with respect to the origin, meaning it mirrors itself after rotating 180 degrees around the origin.
• 😀 A function is odd if f(-x) = -f(x), and this can also be confirmed graphically or numerically.
• 😀 Example of an odd function: f(x) = x³. The graph of x³ is symmetric around the origin.
• 😀 The instructor uses reflections over both the y-axis and x-axis to demonstrate the symmetry of odd functions.
• 😀 Not all functions are even or odd. Some functions, like f(x) = x² - 5x + 2, do not exhibit symmetry with respect to the y-axis or the origin.
• 😀 Functions that are neither even nor odd are said to have no symmetry or parity.
• 😀 In upcoming lessons, the instructor will explain how to verify the parity of a function numerically without relying solely on the graph.