The graph below contains the graphs of two linear functions that are reflections over the line \(y = x\) with \(f(x) = 2x~–~3\) and \(g(x) = \dfrac x2 + \dfrac 32\) . Graph is created using Desmos.com.
- Identify the location of the point of intersection between the two functions and describe why the location makes sense.
- Describe the algebraic relationship between the sets of points identified on each figure.
- Name one more set of points with the same relationship described in Part A.
- Connect each set of points on each figure. What is the relationship between the line drawn from each point and the line \(y=x\) ? What do you notice about the location of each set of points in relationship to the line \(y=x\) ?