Värdemängder

Värdemängder is a Swedish term that translates to "range" in English mathematics. It refers to the set of all possible output values of a function. When you input values into a function, the värdemängd represents all the values that the function can produce.

For a function f: A -> B, where A is the definitionsmängd (domain) and B is the värdemängd (range), the värdemängd is a subset of B. It's the collection of all elements b in B such that there exists at least one element a in A where f(a) = b. In simpler terms, it's what comes out of the function.

Consider the function f(x) = x^2. If the definitionsmängd is all real numbers, then the värdemängd is all non-negative real numbers, as squaring any real number results in a non-negative number. The set of possible outputs is {y | y >= 0}.

The concept of värdemängder is fundamental in understanding function behavior, particularly when analyzing their graphical representations. The projection of a function's graph onto the y-axis visually represents its värdemängd. Understanding the värdemängd helps in determining whether a function is surjective (onto) if its värdemängd is equal to its codomain.