Which function represents the reflection over the x-axis of $f\left(x\right)$?

• A. $f(-x)$
• B. $-f\left(x\right)$
• C. $-f(-x)$
• D. $f\left(x\right)+1$

Answer: (B)

Verified step by step guidance

1. Understand that reflecting a function over the x-axis means flipping its graph vertically. This changes the sign of the output values (the y-values) of the function.
2. Recall that the original function is given as \(f(x)\). To reflect it over the x-axis, you need to multiply the entire function by \(-1\), which changes every output \(f(x)\) to \(-f(x)\).
3. Note that reflecting over the x-axis does not affect the input variable \(x\), so the argument inside the function remains the same.
4. Therefore, the function representing the reflection over the x-axis of \(f(x)\) is \(-f(x)\).
5. Compare this with the other options: \(f(-x)\) reflects over the y-axis, \(-f(-x)\) reflects over both axes, and \(f(x) + 1\) shifts the graph vertically upward by 1 unit, not a reflection.