Which is the graph of the step function \( f(x) \) ? \( f(x)=\left\{\begin{array}{cc}-1, & x<-1 \\ 0, & -1 \leq x \leq 1 \\ 1, & x>1\end{array}\right. \)

To graph the step function \( f(x) \), we can analyze its definition and plot it accordingly. The function is defined as follows: \[ f(x) = \begin{cases} -1 & \text{if } x < -1 \\ 0 & \text{if } -1 \leq x \leq 1 \\ 1 & \text{if } x > 1 \end{cases} \] ### Step-by-step breakdown: 1. **For \( x < -1 \)**: - The function value is \( f(x) = -1 \). - This means that for all values of \( x \) less than -1, the graph will be a horizontal line at \( y = -1 \). 2. **For \( -1 \leq x \leq 1 \)**: - The function value is \( f(x) = 0 \). - This means that for all values of \( x \) from -1 to 1 (inclusive), the graph will be a horizontal line at \( y = 0 \). 3. **For \( x > 1 \)**: - The function value is \( f(x) = 1 \). - This means that for all values of \( x \) greater than 1, the graph will be a horizontal line at \( y = 1 \). ### Points to plot: - At \( x = -1 \), the function jumps from \( -1 \) to \( 0 \). - At \( x = 1 \), the function jumps from \( 0 \) to \( 1 \). ### Graph Description: - The graph will consist of three segments: - A horizontal line at \( y = -1 \) for \( x < -1 \). - A horizontal line at \( y = 0 \) from \( x = -1 \) to \( x = 1 \). - A horizontal line at \( y = 1 \) for \( x > 1 \). ### Visual Representation: While I cannot plot the graph directly, you can visualize it as described above. You can also use graphing software or tools to create the graph based on the piecewise function provided.