1. f(x) = (x + 1)(x − 6) 2. g(x) = 2(x + 1)(x − 6) These functions represent quadratic equations, where f(x) is a standard quadratic function and g(x) is obtained by scaling f(x) by a factor of 2. The graphs of these functions will be similar, but g(x) will be vertically stretched compared to f(x).
The equation of the graph appears to be y = cos(5x). In this trigonometric function, the cosine of 5x is the dependent variable y. The general form of a cosine function is cos(ax), where a represents the frequency or the number of cycles within the interval 2π. In this case, a = 5, indicating that the graph completes five full cycles within the interval 2π.
The cosine function produces a periodic waveform, oscillating between -1 and 1 as 5x varies. The negative sign in front of 57 likely reflects a vertical reflection, causing the graph to be reflected across the x-axis. The amplitude of the cosine function is 1, meaning the graph reaches a maximum of 1 and a minimum of -1. To summarize, the equation y = cos(5x) represents a cosine function with a frequency of 5, an amplitude of 1, and a vertical reflection, resulting in a periodic waveform oscillating between -1 and 1 as 5x varies.