Graphing a Piecewise Function

Each of the component functions is from our library of toolkit functions, so we know their shapes. We can imagine graphing each function and then limiting the graph to the indicated domain. At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.

Figure 25 shows the three components of the piecewise function graphed on separate coordinate systems.

Figure 25 (a) $f\left(x\right)=x^2\text{if }x\le 1;$ (b) $f\left(x\right)=3\text{if 1< }x\le 2;$ (c) $f\left(x\right)=x\text{ if }x>2$

Now that we have sketched each piece individually, we combine them in the same coordinate plane. See Figure 26.

Figure 26