Question

Using complete sentences, explain how to graph the following piecewise function:
y = –x2 if x < 1
y = x if x 1

Answer 1

If you are not looking for mathematical rigor: "Graph both functions simultaneously. Then for the values of x >=1, erase the portion of the y= -x^2 graph. For values of x < 1 erase the portion of the y= x graph."

Answer 2

If you are looking for mathematical rigor, "For values of x less than 1, graph them as if I were graphing y = -x^2. I would have to place an open circle around the point (-1,1) because the function is not continuous here. For the other values, I will graph them as if the function were y = x. I will have to place a closed circle for the point (1,1) because the piecewise function includes x = 1 for the second condition."