Sketch a graph of the piecewise function. Write the domain in interval notation.

f(x)={x+1x−1if x<0if x>0

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:

\[
f(x) = 
\begin{cases} 
x + 1 & \text{if } x < 0 \\
x - 1 & \text{if } x > 0 
\end{cases}
\]

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.

Sketch a graph of the piecewise function. Write the domain in interval notation.

f(x) = {x + 1 if x < 0, x - 1 if x > 0}

Learn how to sketch a piecewise function defined as f(x) = x + 1 for x < 0 and f(x) = x - 1 for x > 0. This detailed solution covers the domain in interval notation, graphing techniques, and identifying discontinuities. Suitable for students in Grades 9-11.

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