If a function is periodic with a period of \(4\), what is \(f(x + 4)\)?

If a function is periodic with a period of \(4\), what is \(f(x + 4)\)?

• A. f(x)
• B. f(x + 4)
• C. 0
• D. f(x - 4)

Answer: (A)

For a function that is periodic with a period of \(4\), it means that the function repeats its values every \(4\) units along the \(x\)-axis. Therefore, for any value of \(x\), the output of the function at \(x\) is the same as the output at \(x + 4\). This relationship can be expressed mathematically as: \[ f(x + 4) = f(x) \] This demonstrates that the value of the function at \(x + 4\) is equivalent to the value at \(x\), reinforcing the definition of periodicity. Consequently, when asked what \(f(x + 4)\) is, the correct answer is indeed \(f(x)\).

For a function that is periodic with a period of (4), it means that the function repeats its values every (4) units along the (x)-axis. Therefore, for any value of (x), the output of the function at (x) is the same as the output at (x + 4). This relationship can be expressed mathematically as:

[ f(x + 4) = f(x) ]

This demonstrates that the value of the function at (x + 4) is equivalent to the value at (x), reinforcing the definition of periodicity. Consequently, when asked what (f(x + 4)) is, the correct answer is indeed (f(x)).