This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Until, let's knock this out. 3.3.1 The period of a trigonometric graph is the length of one complete cycle before the graph starts to repeat itself. 3.3.2 To draw the graphs of f(x) = x and h(x) = 2 x on the same set of axes for 0^ x 360^: Set up axes: Draw an x-axis labeled from 0^ to 360^ (with markings at 90^, 180^, 270^) and a y-axis labeled from -2 to 2. Graph f(x) = x (standard cosine wave): Plot points: (0^, 1), (90^, 0), (180^, -1), (270^, 0), (360^, 1). Draw a smooth curve connecting these points. Graph h(x) = 2 x (sine wave with amplitude 2): Plot points: (0^, 0), (90^, 2), (180^, 0), (270^, -2), (360^, 0). Draw a smooth curve connecting these points. Label each graph clearly, e.g., "f(x) = x" and "h(x) = 2 x". 3.3.3 The amplitude of f(x) = x is the absolute value of the coefficient of x. For f(x) = 1 · x, the amplitude is |1|. The amplitude of f(x) is 1. 3.3.4 The range of h(x) = 2 x is determined by its amplitude. The general form A x has a range of [-A, A]. For h(x) = 2 x, the amplitude is 2. The range of h(x) is [-2, 2] or -2 y 2. What's next?