Which rules define the function graphed below

y = x+2 ; y = 5

Explanation:
1- getting the function from x = 0 till x = 3:
We can note that this part of the graph is a linear function. This means that is has a general form:
y = mx + c where m is the slop and c is the y-intercept (value of y at x=0).
For the slope, we will use the points (0,2) and (3,5) to calculate it as follows:
m = (y2-y1)/(x2-x1) = (5-2)/(3-0) = 1
For the y-intercept, we can note that at x=0, the value of y is 2. 
This means that the equation of the first part of the graph is:
y = x + 2

2- getting the function from x=3 till the end of the graph:
We can note that this part of the graph has a constant function.
Regardless the value of x, the value of y is always 5.
This means that the equation for this part is:
y = 5

From parts 1 and 2, we can deduce that the correct functions are:
y = x+2 ; y = 5

Hope this helps :)