Is x = 7 a function?

Jul 29, 2015

$x = 7$ is not a function!

Explanation:

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output (See https://en.wikipedia.org/wiki/Function_%28mathematics%29#cite_note-1 for more information).

In most graphs with a x-axis and a y-axis, there is only one y-value for every x-value. Take for example $y = x$:
graph{y=x [-10, 10, -5, 5]}
Notice that as you keep going across the graph, the line always continues through the $x$-axis, but with one $y$-point defined in each point in addition to a definable slope.

However, $x = 7$ is a vertical line that continues up and down the $y$-axis in one location, $x = 7$! Thus it violates the law of a function since numerous of points are defined in a single point of the $x$-axis.

A vertical line test is often best used to determine a function of a curve. Common equations are inverse trigonometry equations like $y = {\tan}^{-} 1 x$ and other random functions. If the vertical line crosses two or more points on a graph, then it is considered not a function, unless a section of the curve is defined with a limit that is continuous with a definable slope.

Khan Academy has a good series on understanding functions in depth: