Learning Objectives:

__Math Tutoring on Determining if a Relation is a Function__

A **function** (a set of **ordered pair**) is a special relationship where each input has a single output. The **domain** of a function is a set of all possible values for the **input variable** also known as the **independent variable** which is often **x. **The **range** of a function is a set of all possible values for the **output variable **or** the dependent variable **which is often **y.** In math tutoring for **Vertical Line Test,** we imagine a vertical line is drawn through the graph. If the vertical line only touches the graph at **one point**, then it is a **function**. If the vertical line touches in **more than one point**, then it is **NOT a function**. Think of the **vertical line test** this way. The points on the graph of a function **f **have the form **(x, f(x)),** so once you know the first coordinate, the second is determined. When a vertical line is placed across the **graphing plot** of this relation, it intersects the **graph** more than once for some values of **x.** If a **graph** shows **two or more intersections **with a vertical line, then an **input (x-coordinate)** can have more than one **output (y-coordinate).** This is the case when** y** is not a **function of x**.

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**Hook Questions:**

*1. **Which graph is a function?*

*2. **Is a vertical line a linear function? *

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