Question

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

Answer 1

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