Graphing Piecewise Functions

Pre-Calculus · Axiom Academy

EXAMPLE Graphing Piecewise Functions Graph a function defined by different rules on different intervals — and read off its key features. Graph the piecewise function below, then identify its boundary points, endpoint types, and where it is continuous. The graph rises along the line, curves through the parabola to , then jumps down to the open point and runs flat. Nice work — you graphed a three-rule piecewise function and read its features straight off the picture. One rule per interval: graph each piece only over the x -values it owns, never beyond. Endpoints carry the inequality: a or gives a closed (filled) dot; a or gives an open (hollow) dot. When two pieces land on the same point, the closed dot wins. Continuity is "do the pieces meet?": here the line and parabola agree at x=-1 (both 1 ), so it's continuous there; the parabola ends at 4 while the constant is 3 , so x=2 is a jump. Same recipe scales to any piecewise function: split by interval, fix the endpoints, then check where the pieces connect.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.