The graph represents the piecewise function:

We have two pieces of the piecewise function shown.

Let us try to find equation for each.

part first:

here the graph is a straight line parallel to x axis passing through y at 4

So equation of the line parallel to x axis is given by y=a, where a is y intercept.

so equation for first part is y=4

Second part:

here graph is a slant line with coordinates (3,2) and (5,4)

so let us first find slope of this line using the formula:

plugging values:

slope = 1

now we use point slope form to get the required equation

y=x-1

Answer :