# Why does the vertical line test work?

##### 1 Answer

Please read the explanation.

#### Explanation:

Let us say we have a **graph** drawn for a mathematical relation.

This is a mathematical relation, as for every value of

To check whether this graph is a **function**, a **Vertical Line Test** can be used.

Let us examine the following graph drawn for the mathematical relation:

Can you observe the **vertical lines** drawn for various values of

All of these **vertical lines intersect the graph at one point only**.

If there is just one point of intersection,

that would mean,

**for every x-value, there is just one unique y-value**.

This property proves that the given mathematical relation

is a **mathematical function**.

Hence, the **vertical line test** works in determining whether a given relation is a function.

**Let us try one more mathematical relation:**

This mathematical relation creates a parabola and the parabola is **symmetric** about the **x-axis**, at

This mathematical relation

as the **vertical line test** fails.

Hope it helps.