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# What are examples of functions in algebra 2?

**In Algebra 2, a function is a relation where every input has only one output.** A relation is defined as a combination of inputs and outputs

To form a relation, it is necessary to write all the inputs and outputs as ordered pairs. For example, in an ordered array (0, 1, 2, 3) one can have a relation in the form of (0,4), (1,5), (2,6) and (3,7).

A function is a relation where very input has one and only one output. Normally in relations, a single input could have multiple outputs. But with functions, a single input must have a single output.

A function could be linear, quadratic, cubic, polynomial, rational or irrational. Y = mx +c is an example of a linear function, whereas f(x) = ax2 + bx + c is a quadratic function.

Some examples of functions in Algebra 2 are Y = 3x + 1, which is a linear function, F(x) = 10x + 13, which is also a linear function and Y = 3x2 + 2x +10, which is a quadratic function.

Functions are also known as algebraic functions. One can apply addition, multiplication, subtraction and division to algebraic functions. Functions can also be represented with the help of graphs.

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