How to Graph a Piecewise Function

Worked example

Suppose f(x) = x + 2 for x < 1 and f(x) = 4 − x for x ≥ 1. Draw the first line only to the left of x = 1. Put an open circle at (1, 3) for that piece. The second piece includes x = 1, so the point (1, 3) is filled.

Try another example

Now use f(x) = x + 2 for x < 1 and f(x) = 5 − x for x ≥ 1. The left piece ends with an open circle at (1, 3), while the right piece starts with a filled circle at (1, 4).

Check your result

If your calculator only plots unrestricted expressions, plot each formula for reference and copy only the section belonging to its interval. At a breakpoint, check which inequality includes equality.