Problem 61 - College Algebra

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, negate the function's equation, resulting in \(-f(x)\). In other words, multiply every y-coordinate by -1.

Step 1: Understand the concept

The x-axis is the horizontal axis on a coordinate plane. Reflecting a point across the x-axis requires changing the sign of its y-coordinate, essentially flipping the point vertically.

Step 2: Apply to Function's Equation

Let's generally formulate a function as \(f(x)\). To reflect the entire graph of this function across the x-axis, the y-values of the function have to change. This is achieved by negating the function, i.e., the reflected function would be \(-f(x)\). This means that every output (y-coordinate) of the function is multiplied by -1, effectively flipping the function over the x-axis.