Problem 131 - Precalculus Essentials

Question

What must be done to a function's equation so that its graph is reflected about the \(x\) -axis?

Step-by-Step Solution

Answer

To reflect a function's graph about the \(x\)-axis, change the function's equation from \(f(x)\) to \(-f(x)\).

Step 1: Understand Reflection

Reflection of a graph about the \(x\)-axis means that the position of every point of the original graph is reversed concerning the \(x\)-axis, i.e., the sign of the \(y\)-coordinate of every point on the original graph changes.

Step 2: Implementing Reflection

To apply reflection to a function's equation, one needs to change the sign of the function. If the original function's equation is \(f(x)\), then the reflected function's equation will be \(-f(x)\). This way, for every \(x\), the sign of the corresponding \(y\)-value changes, thus reflecting the graph about the \(x\)-axis.