A function is often represented by f(x) where f is just a letter (can be anything, upper or lowercase). And x is an independent variable which means it's not dependent on anything. Then follows an equals sign and the actual definition of the function in terms of x. Often "(x)" is omitted so we can have y= instead of f(x)=, or we can write y=f(x) where f(x) has been defined. That just means y is another name for f(x).
A function can also be represented as a mapping: f:x→y. This means that f is an operation performed on x to be assigned to a dependent variable y. Dependent just means y depends on x. Examples are f(x)=2x+3. So for some value assigned to x there is one and only one value for y. If x=2 then f(x)=7 which can also be written f(2)=7.