What are the differences among expressions, equations, and functions? Provide examples of each.
(1) An expression does not contain delimiters such as `=,<,>,<=,>=,cong` etc... You can simplify expressions (e.g. combine like terms, eliminate negative exponents, eliminate parantheses, etc...) or evaluate expressions (e.g. substitute given values for variables.)
Examples of expressions include `2x+3,3x^2+2x-4,ln(2x),5,pi,e^(i pi)`
(2) Equations are expressions separated by an equals sign =. Mathematically, this implies that each side of the equation has the same value.
You can solve equations (e.g. find the value(s) of the variable(s) that make the equation true.)
Examples include `2x=4,4=4,2x^2+3x-4=0,x^2y+xy^3=xy,sin(x)=sqrt(3)/2` etc...
(3) A function is a type of relation where each input is assigned exactly one output. Functions are often represented as equations (e.g. `y=2x+3` where y is a function of x or `f(x)=2x+3` where the function is written in function form.) But functions can be represented by their graphs, a set of ordered pairs, a mapping diagram, a verbal description, etc...