Best Answer

A function cannot have multiple outputs (y-values) for any given input (x-values). For example, y=2x+3 is a function because no mater what number x represents, there is a single, unique y-value (When x=3 y=9 ). In other words, you can never have two (or more) y-values that correspond to a single x-value. Therefore, a vertical line, for example x=2, cannot be a function because it has an infinite amount of y-values for a single x-value. A horizontal line is a function because there is only one y-value for any given x-value. For example, y=3. No mater what x-value is used, there is only one y-value possible (in this case, y will always equal 3). I am, of course, referring to the cartesian coordinate system, also known as the rectangular coordinate system.

Q: Why can a horizontal line be a graph of a function but a vertical line cannot?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Yes the graph of a function can be a vertical or a horizontal line

Normally the input is on the horizontal axis and the output on the vertical axis.

Time on horizontal, Distance on Vertical

The convention for an x-y graph is as follows: y | | |_____ x where the x-axis is horizontal and the y-axis is vertical.

Cannot exist. And a vertical graph is simply a vertical graph!

Related questions

Yes the graph of a function can be a vertical or a horizontal line

Yes the graph of a function can be a vertical or a horizontal line

Yes the graph of a function can be a vertical or a horizontal line

The vertical line test can be used to determine if a graph is a function. If two points in a graph are connected with the help of a vertical line, it is not a function. If it cannot be connected, it is a function.

Not quite. You can use a vertical line test on the graph of the inverse mapping, OR you can use a horizontal line test on the original graph. The horizontal line test is used in the same way.

Normally the input is on the horizontal axis and the output on the vertical axis.

Along the horizontal axis, or the vertical axis if there are two variables that cannot be controlled.

A graph is a function if every input (x-value) corresponds to only one output (y-value). One way to check for this is to perform the vertical line test: if a vertical line intersects the graph at more than one point, the graph is not a function.

Time on horizontal, Distance on Vertical

Vertical transformations involve shifting the graph up or down, affecting the y-values, while horizontal transformations involve shifting the graph left or right, affecting the x-values. Vertical transformations are usually represented by adding or subtracting a value outside of the function, while horizontal transformations are represented by adding or subtracting a value inside the function.

If for every point on the horizontal axis, the graph has one and only one point corresponding to the vertical axis; then it represents a function. Functions can not have discontinuities along the horizontal axis. Functions must return unambiguous deterministic results.

The convention for an x-y graph is as follows: y | | |_____ x where the x-axis is horizontal and the y-axis is vertical.