Question

in all, eulers legacy included the introduction of the concept of functions, as well as the proper way to write them within a mathematical formula by using the notation f(x). before his formalization of the notation, functional relationships were referred to by just one letter, f, or with greek letters omitting the parentheses, φx. in fact, euler spelled out much of the mathematical notation we use today, including the letter \e\ for the base of the natural logarithm (also known as eulers number), the letter \i\ to denote the imaginary unit, and the greek letter \σ\ for summations. he also encouraged the use of the greek letter \π\ to signify the ratio of a circles circumference to its diameter. which mathematical concepts did eulers legacy include? check all that apply. the notation for the imaginary unit the idea of a functional relationship the formalization of function notation the definition of a circles circumference the notation for the base of the natural logarithm

Explanation:

Euler introduced the notation for the imaginary unit ($i$), formalized function notation ($f(x)$), and the notation for the base of the natural logarithm ($e$). He also contributed to the idea of functional relationships. The definition of a circle's circumference was known before Euler and not his main contribution.

Answer:

the notation for the imaginary unit, the idea of a functional relationship, the formalization of function notation, the notation for the base of the natural logarithm