A function is a mathematical relationship between inputs (also called "arguments" or "parameters") and the resulting output. It can also be thought of as a machine that takes in certain inputs and produces a specific output.
To define a function, you need to specify the input(s), the mathematical operations or formula to be performed on the input(s), and the resulting output. This is typically done using functional notation, where the function is named and the input(s) are surrounded by parentheses.
A function is a mathematical relationship between inputs and outputs, while a variable is a placeholder for a value. In other words, a function takes in inputs and returns outputs, while a variable simply holds a value.
Yes, a function can have multiple inputs. This is known as a multivariate function. The number of inputs a function has is known as its "arity". Some functions may have a fixed number of inputs, while others may have a varying number of inputs depending on the context.
The domain of a function is the set of all possible inputs, while the range is the set of all possible outputs. To determine the domain and range of a function, you can use mathematical techniques such as finding the intercepts, determining the intervals where the function is defined, or using algebraic methods such as finding the inverse function. It is important to note that the domain and range of a function may be limited by the context in which the function is being used.