Question

which is the graph of the step function f(x)?
f(x) = \

$$\begin{cases}-1, & x < -1 \\\\ 0, & -1 \\leq x \\leq 1 \\\\ 1, & x > 1\\end{cases}$$

Explanation:

Step1: Analyze first - part of function

For \(x < - 1\), \(f(x)=-1\). This is a horizontal line at \(y = - 1\) with an open - circle at \(x=-1\) (since \(x\) is strictly less than \(-1\)).

Step2: Analyze second - part of function

For \(-1\leq x\leq1\), \(f(x) = 0\). This is a horizontal line at \(y = 0\) with closed - circles at \(x=-1\) and \(x = 1\) (because of the inclusive inequalities).

Step3: Analyze third - part of function

For \(x>1\), \(f(x)=1\). This is a horizontal line at \(y = 1\) with an open - circle at \(x = 1\) (since \(x\) is strictly greater than \(1\)).

Answer:

The graph consists of a horizontal line \(y=-1\) for \(x < - 1\) (open - circle at \(x=-1\)), a horizontal line \(y = 0\) for \(-1\leq x\leq1\) (closed - circles at \(x=-1\) and \(x = 1\)), and a horizontal line \(y = 1\) for \(x>1\) (open - circle at \(x = 1\)).