Final answer:
The period of a function is the length of one complete cycle on a graph, which can be calculated differently depending on the context. For trigonometric functions, it is found using T = 2π / |B|, and for physical oscillations like a pendulum, T = 2π √(l/g). In AC electricity, T can also be calculated as T = 1/f or T = 2π / ω.
Step-by-step explanation:
The period of a function in a graph describes the length of one complete cycle of the graph. For example, in trigonometry, the period of the sine or cosine function is the distance along the x-axis after which the wave pattern begins to repeat. In practical terms, for a sine or cosine function of the form y = A sin(Bx + C) + D or y = A cos(Bx + C) + D, the period T is calculated using the formula T = 2π / |B|, where B is the coefficient of x inside the trigonometric function.
In the context of physics, particularly when discussing pendulums or oscillatory motion, the period equation can relate to the time it takes to complete one cycle of motion. An example is the simple pendulum equation T = 2π √(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity.
When dealing with alternating current (AC) electricity or wave phenomena, the period T can also be found using the relationship T = 1/f, where f is the frequency. The period is also represented as T = 2π / ω, with ω being the angular frequency.
In graphing calculators and software such as the PhET Equation Grapher, you may adjust constants to observe different polynomial functions and their graphs, which could include periodic phenomena depending on the equation.