The Vertical Line Test
You can check whether a graph represents a function by using the vertical line test.
The test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.
Example :
This graph does not represent a function: for example, the vertical line $x=1$ intersects it in three places. 
This graph does represent a function, since any vertical line intersects the graph exactly once, except $x=0$ , which doesn't intersect it at all. 

Consider the graph shown.
You can see that no vertical lines pass through two points on the graph.
Note that $(2,0)$ and $(1,2)$ are open points and are not on the graph. So, the vertical lines $x=2$ and $x=1$ pass through only one point on each of the line segments.
Therefore, the graph shown is of a function.
The step function can be defined as:
$\begin{array}{ccc}\begin{array}{l}y=\frac{1}{2}x+1\\ y=x1\\ y=5\end{array}& \begin{array}{l}\\ \\ \end{array}& \begin{array}{l}6\le x<2\\ 2\le x<1\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}1\le x\le 6\end{array}\end{array}$
The domain of the function is $6\le x\le 6$ and the range is $2\le y\le 5$ .