Functions, domains and introductory graphs (quadratic function emphasis)

Notes

• Function Definitions and Notations y = x^{-1} = x' y = αx² + bx + c • Function Table and Domain-Ranges | Function | Domain (x) | Range (y) | |----------------------|------------------------|------------------------------| | y = x³ | b = c = [0, ∞) | (0, ∞) | | y = 1/x | y = √x = x^{1/2} | (−∞, 0) ∪ (0, ∞) | | y = √x = x^{1/2} | y = 4 - x² | (0, [0, ∞)) | | y = 4 - x² | N(4 - x) + function | (0, [0, 1)) | | N(4 - x) = (4 - x) | | | • Storage Area 物品存放处 --- • Function Value and Graph Interpretation y = f(x) Function Value f(1) f(x) - f(2, f(2)) Scale Origin FIGURE 1.4: If f(x) lies on the graph of f, then the value y = f(x) is the height of the graph above the point if below if f(x) is negative. Slide 8 of 77 物品存放处 --- • Quadratic Function and Graph y = x² x: -2, -1, 0, 1, 2 Values: - For x = -2: 4 - For x = -1: 1 - For x = 0: 0 - For x = 1: 1 - For x = 2: 4 Additional expression: (+ 3/2)² = 9 Subtraction: -4 General quadratic form: y = a x² + b x + c where a = 1; b = 0; c = 0 • Graph of the Function FIGURE 1.9: Graph of the function in Example 2. Thomas' Calculus, 14th Edition Slide 9 of 77 --- This completes the structured and corrected version of the provided content, maintainin...