Final answer:
The period of a tangent function is the time it takes for one complete cycle, which is typically π radians or 180 degrees. It is the inverse of the frequency, not the amplitude, frequency, or range of the function.
Step-by-step explanation:
The period of a tangent function refers to the time it takes for one complete cycle of the function to occur. In relation to a sine or cosine function, the period is the distance on the x-axis between two consecutive points where the function begins to repeat its pattern. For a tangent function, this is typically π radians or 180 degrees, because the tangent function repeats itself every π radians.
It's important to differentiate the period from amplitude and frequency, which are different characteristics of periodic functions. Amplitude is the distance between the resting position and the maximum displacement of the wave, which does not apply to the tangent function as it has no maximum displacement; it extends indefinitely. Frequency is the number of waves passing by a specific point per second, and it is the inverse of the period. The range of a function represents all the possible output values (y-values) the function can take, which for tangent includes all real numbers except the discontinuities where the function is undefined.
To summarize, the period is the inverse of the frequency (Choice C), not the amplitude, frequency, or range of the function.