Piecewise Function Grapher

Algebra 2 · Axiom Academy

LESSON Piecewise Function Grapher Learn how to build, graph, and evaluate piecewise functions by understanding how different pieces connect at boundary points. 1. What is a Piecewise Function? Here's a simple example that demonstrates the concept: This function has two pieces: one for x-values less than 2, and another for x-values greater than or equal to 2. The boundary point is at x = 2 . Each piece is a restriction : take the whole curve y = x , and keep only the part where ; take the whole line y = 4 , and keep only the part where . Here the left piece climbs toward the height 2 while the right piece sits at 4, so the graph jumps at the boundary — Step 5 turns that observation into a test. 2. Building from Component Parts Let's see how to construct a piecewise function by graphing each piece separately, then combining them into one complete function. Each piece is graphed only over its specified domain. The boundaries at x = -1 and x = 2 determine where we switch from one formula to another. The middle piece uses at both ends, so it owns x = -1 and x = 2 outright — the outer pieces use strict and and stop just short. Check what happens at each seam: Left piece approaches (-1) + 2 = 1 . Middle piece gives (-1)^2 = 1 . Same value, so the hole is filled: one closed dot at (-1, 1) and no break. Middle piece gives 2^2 = 4 . Right piece approaches -(2) + 6 = 4 . Same value again: one closed dot at (2, 4) , and the graph stays unbroken. 3. Evaluating Piecewise Functions

This is the written version of the interactive lesson above. See the full Algebra 2 course.