### Home > CALC > Chapter 1 > Lesson 1.2.1 > Problem 1-21

1-21.

*x* = 1 can be called, informally, the Boundary Point of the piecewise function *f*(*x*). This is because *x* ≤ 1 is the location where the left and the right pieces switch.

*f*(0) and *f*(1) are on the left side of the Boundary Point, *f*(3) is on the right side of the Boundary Point.

*f*(0) = 4 − 3(0) = 4 LEFT PIECE *f*(1) = 4 − 3(1) = 1 LEFT PIECE *f*(3) = (3)² = 9 RIGHT PIECE

The Boundary Point is *x* ≥ 3. So *f*(1) lies on the left side of the piecewise function while *f*(3) and *f*(9.4) lie on the right.

This function has two boundary points and three pieces: a left piece, a middle piece and a right piece. On which piece do the points f(−3), f*f*(0), *f*(0.5) and *f*(4) lie?