To determine whether

*y* is a function of

*x*,
given a graph of a relation, use the following criterion: if every

*vertical line*
you can draw goes through only 1 point,

*y* is a function of

*x*.
If you can draw a vertical line that goes through 2 points,

*y* is not a function of

*x*.
This is called the

vertical line test.

*Example 1*: In the following graph,

*y*
is a function of

*x*:

*Passes Vertical Line Test *

*Example 2*: In the following graph,

*y*
is not a function of

*x*:

**Fails Vertical Line Test**
To determine whether

*x* is a function of

*y*,
given a graph of a relation, use the following criterion: If every

*horizontal line*
you can draw passes through only 1 point,

*x* is a function of

*y*.
If you can draw a horizontal line that passes through 2 points,

*x* is not a function of

*y*. This is called the

horizontal line test.

*Example 1*: In the following graph,

*x*
is a function of

*y*:

**Passes Horizontal Line Test**
*Example 2*: In the following graph,

*x*
is not a function of

*y*:

**Fails Horizontal Line Test**