Question

Is `x = 7` a function?

Answer 1

`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^-1x` 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:
https://www.khanacademy.org/math/algebra/algebra-functions.