Is #x = 7# a function?

1 Answer
Jul 29, 2015

#x=7# is not a function!


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 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: