 ## Tutoring on Introduction to Functions: Function Basics

Learning Objectives:

#### Understand and Graph Functions.

 Introduction to Functions/Functions Basics   A Relation is any set o ordered pairs. A Function is a relation in which every input value is paired with exactly one output value. So a function is a relation, but it is a special relation in which every input value is paired with exactly one output value. Because the input variable is often x and the output variable is often y, sometimes the definition of a function as a relation in which every x-value is paired with exactly one y-value. One way to represent the relationship between the input and output variables in a relation or function is by the means of a table of values. So by analyzing the table, we’re going to determine if every input value is paired with exactly one output value. If it is, it is a function. But if we have an input that is paired with more than one output value, it is not a function. It is still a relation, but not a function. The Vertical Line Test tells us, if all vertical lines intersect the graph of a relation in at most one point, that means at zero points or one point, the relation is also a function, meaning one and only one output exists for each input. If any vertical line intersects the graph of a relation a more than one point, the relation fails the test and is not a function. More than one value exists for some or all of the input values.         Hook Questions         1.What is the difference between Relation and Function? 2.How can you determine whether a relation is a function or not? 3.What is Vertical Line Test?

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