Definition of Function
Definition of function is a foundational Grade 7 math concept from Yoshiwara Intermediate Algebra. A function is a rule that assigns to each input exactly one output. Students learn formal definitions using domain, codomain, and range, and distinguish functions from non-functions.
Key Concepts
Property A function is a relationship between two variables for which a exactly one value of the output variable is determined by each value of the input variable . The variable used for the input is the input variable , and the variable for the output is the output variable .
Examples The area $A$ of a circle is a function of its radius $r$, given by the formula $A = \pi r^2$. For any radius you choose, there is only one possible area.
The total cost of buying concert tickets is a function of the number of tickets purchased. If each ticket costs 50 dollars, the cost $C$ for $n$ tickets is $C = 50n$.
Common Questions
What is a function in mathematics?
A function is a rule that assigns to each element of the domain (input) exactly one element of the range (output). Each input has one and only one output.
How do you know if a relation is a function?
Check that every input maps to exactly one output. If any input has two different outputs, the relation is not a function.
What is the domain of a function?
The domain is the set of all valid input values for the function.
What is the difference between range and codomain?
The codomain is the set of all possible outputs, while the range (or image) is the set of outputs actually produced by the function.