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abhip
- 9
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f(x)+f(x+4)=f(x+2)+f(x+6) where all functions are real valued
The period of a function is the length of the interval over which the function repeats itself. In other words, it is the distance between two consecutive peaks or troughs on a graph of the function.
To find the period of a function, you need to identify the value of the variable that causes the function to repeat itself. This is usually found in the argument of a trigonometric function or within a set of parentheses in an algebraic function. Once you have identified this value, you can use it to calculate the period using the appropriate formula.
The period and frequency of a function are inversely related. The period is the length of time it takes for a function to complete one full cycle, while the frequency is the number of cycles that occur in one unit of time. In other words, the period is the reciprocal of the frequency.
No, a function cannot have a negative period. The period is always a positive value, as it represents the distance between two consecutive repetitions of the function. However, a function can have a negative frequency, which indicates a reversal of the direction of the function's graph.
The period of a function determines the frequency of its wave-like pattern. A shorter period results in a higher frequency, causing the graph to appear more compressed or "squished" horizontally. Conversely, a longer period leads to a lower frequency and a wider, more spread out graph.