# Question #c3676

Nov 20, 2016

See explanation.

#### Explanation:

A function $y = f \left(x\right)$ is an assignment where for every value of $x$ there is only one corresponding value of $f \left(x\right)$

Explanation 1

The vertical line goes through ever point $\left({x}_{0} , y\right)$ for a constant ${x}_{0}$ and all real $y$. This means that for one argument ${x}_{0}$ there are infinitely many values $y$ which does not fulfill the condition defining a function $y = f \left(x\right)$

Explanation 2

Other way to justify such imposibility is that for every linear function $y = m x + b$ $m$ is the value of tangent of angle between the graph and $X$ axis.

If we graph a vertical line we see that the angle between the graph and $X$ axis is ${90}^{o}$, but $\tan 90$ does not exist therfore there is no possible value of $m$ for such graph.