Lamar’s teacher extended the graph as shown below and asked lamar to write the function for the graph shown below using f(x) for the function name

We assume you want to know what Lamar should have written as the definition of f(x).

We know the points (-3, -2) and (2, 3) are on the graph. These differ in both the x-direction and the y-direction by 5, so the slope of the line is 5/5 = 1.

Since the line goes through point (-3, -2) with slope 1, we can use the point-slope form of the equation of a line:
   f(x) = 1(x -(-3)) +(-2)
   f(x) = x +1 . . . . . . . . . . after simplification