__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?** |