functions nd graphs gen math

What is a relation?

A relation from a set X to a set Y is a subset of the Cartesian product X \times Y. The set X is called the domain of the relation, and the set Y is called the codomain.

What is a function?

A function f from a set X to a set Y is a relation from X to Y with the following properties:

1. For every x \in X, there exists y \in Y such that (x, y) \in f.
2. If (x, y) \in f and (x, z) \in f, then y = z.

What is the domain of a function?

The set of all possible input values (x-values) which produce a valid output from a function.

What is the range of a function?

The set of all possible output values (y-values) which result from using all possible input values in the domain of a function.

What is a relation?

A relation from a set X to a set Y is a subset of the Cartesian product X \times Y. The set X is called the domain of the relation, and the set Y is called the codomain.

What is a function?

A function f from a set X to a set Y is a relation from X to Y with the following properties:

1. For every x \in X, there exists y \in Y such that (x, y) \in f.
2. If (x, y) \in f and (x, z) \in f, then y = z.

What is the domain of a function?

The set of all possible input values (x-values) which produce a valid output from a function.

What is the range of a function?

The set of all possible output values (y-values) which result from using all possible input values in the domain of a function.

What is a linear function?

A function that assigns a unique output value to each input value. It is visualized as a straight line on a graph and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

What is a quadratic function?

A function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a \neq 0. The graph of a quadratic function is a parabola.