Final answer:
The operation that involves horizontally mirroring intervals in mathematics is called the reflection.
Step-by-step explanation:
Reflection is a transformation that flips a figure over a line called the line of reflection. When a figure is reflected over a horizontal line, the x-coordinates of corresponding points remain the same, but the y-coordinates change sign, effectively mirroring the figure horizontally.
For example, if we have the interval [1, 5] and reflect it over the x-axis, we would get the interval [-5, -1], which is the horizontally mirrored version of the original interval.