Graph the function. \[ f(x)=\left\{\begin{array}{ll} x^{2}-9, & \text { if } x<-1 \\ 0, & \text { if }-1 \leq x \leq 1 \\ x^{2}+9, & \text { if } x>1 \end{array}\right. \]

Step 1 ：First, we need to understand the function. It is a piecewise function, which means it is defined by different formulas for different intervals of the input \(x\).

Step 2 ：The function is defined as \(x^{2}-9\) for \(x<-1\), as \(0\) for \(-1 \leq x \leq 1\), and as \(x^{2}+9\) for \(x>1\).

Step 3 ：Let's graph each piece of the function separately.

Step 4 ：For \(x<-1\), the function is \(x^{2}-9\). This is a parabola opening upwards, shifted down by 9 units. It is only defined for \(x<-1\), so we only draw the left part of the parabola.

Step 5 ：For \(-1 \leq x \leq 1\), the function is \(0\). This is a horizontal line at \(y=0\), only drawn between \(x=-1\) and \(x=1\).

Step 6 ：For \(x>1\), the function is \(x^{2}+9\). This is a parabola opening upwards, shifted up by 9 units. It is only defined for \(x>1\), so we only draw the right part of the parabola.

Step 7 ：Putting all these pieces together, we get the graph of the function.

Step 8 ：The graph starts with the left part of the parabola \(x^{2}-9\) for \(x<-1\), continues with the horizontal line at \(y=0\) for \(-1 \leq x \leq 1\), and ends with the right part of the parabola \(x^{2}+9\) for \(x>1\).

Step 9 ：This completes the graph of the function.