what are functions? practice and quick check tcah
In mathematics, a function is a relationship in which every input (or independent variable) is associated with a unique output (or dependent variable).
Functions can be represented by equations, graphs, or tables, and they are used to model real-world phenomena such as population growth, economic trends, and physical systems.
In order to be considered a function, each input must have exactly one output (i.e. no two different inputs can have the same output), and the function must define a complete mapping between the inputs and outputs within its domain.
For example, the equation f(x) = 2x represents a function where the input x is multiplied by 2 to produce the output f(x).
To check if a relationship is a function, you can use the vertical line test (if no vertical line intersects the graph of the relationship more than once, then it is a function) or check if each input has a unique output in the corresponding table or equation.