It looks like you're asking for help with a piecewise function, but the formatting seems unclear. Based on what you provided, the function seems to be a piecewise function with different definitions depending on the value of $x$. Let me clarify it for you and sketch the graph.

Here’s a possible interpretation of the function:

\begin{cases} x + 1 & \text{if } x < 0 \\ x - 1 & \text{if } x > 0 \end{cases}$$ To summarize: 1. For $$x < 0$$, $$f(x) = x + 1$$. 2. For $$x > 0$$, $$f(x) = x - 1$$. 3. There seems to be no definition for $$x = 0$$, so $$f(x)$$ is undefined at $$x = 0$$. ### Domain Since the function is defined for all $$x < 0$$ and $$x > 0$$, but not at $$x = 0$$, the domain in interval notation is: $$\text{Domain: } (-\infty, 0) \cup (0, \infty)$$ ### Sketching the Graph - **For $$x < 0$$**: The line is $$f(x) = x + 1$$, which is a linear function with a slope of 1 and a y-intercept at $$y = 1$$. - **For $$x > 0$$**: The line is $$f(x) = x - 1$$, which is a linear function with a slope of 1 and a y-intercept at $$y = -1$$. - **At $$x = 0$$**: The function is undefined, so there will be a hole in the graph at $$x = 0$$. Let me know if you'd like further details or if you want me to plot the graph. Here are 5 relative questions that build upon this topic: 1. How do we graph piecewise functions with more than two intervals? 2. What is the difference between continuous and discontinuous piecewise functions? 3. How do we find the range of a piecewise function? 4. How do you determine if a piecewise function has a jump discontinuity? 5. Can piecewise functions have more than one point of discontinuity? **Tip**: When graphing piecewise functions, always check if there is continuity or if the function has undefined points at the boundaries.