Epigraph (mathematics)

Imagine you are trying to solve a puzzle, and you need to use a special tool to help you. That tool is called an epigraph.

In math, an epigraph is a kind of tool that helps you solve problems that involve functions. A function is like a machine that takes in a number and gives you another number as the output.

Now, let's say you want to figure out what numbers can be plugged into a function to solve a certain problem. This is where the epigraph comes in.

The epigraph is basically a way to look at a function from a different angle. Instead of looking at the values of the function, you look at the set of points on a graph where the function is "below" a certain number.

For example, let's say you have a function that is a line on a graph. The epigraph of that line would be the area above the line. This helps you solve problems involving inequalities, or where you need to find the highest or lowest possible value of the function.

So, to sum it up: An epigraph is a tool that helps you solve problems involving functions by looking at the set of points on a graph where the function is below a certain number.