# Graphing Piecewise Functions, Domain & Range - Limits, Continuity, & Absolute Value , | Summary and Q&A

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August 23, 2016
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The Organic Chemistry Tutor
Graphing Piecewise Functions, Domain & Range - Limits, Continuity, & Absolute Value ,

## TL;DR

Learn how to graph piecewise functions, identify their domain and range, and analyze their limits and continuity.

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### Q: How do you graph a piecewise function?

To graph a piecewise function, graph each part separately based on the given conditions, and then combine them into a single graph. Plot the points for each part and connect them accordingly. Remember to pay attention to open and closed circles for endpoints.

### Q: What does the domain of a function represent?

The domain of a function represents all the allowed x values for the function. It is the set of real numbers for which the function is defined. In the case of a piecewise function, the domain may have different restrictions for each part of the function.

### Q: How do you determine the range of a piecewise function?

To determine the range of a piecewise function, consider the y values for the corresponding x values in the domain. Identify the lowest and highest y values present in the function. The range includes all possible y values between the lowest and highest values but may exclude certain values based on open or closed circles.

### Q: What is the significance of a jump discontinuity in a graph?

A jump discontinuity occurs when there is a sudden change in the graph, resulting in a gap between the two parts of the function. It indicates a discontinuity or a jump in the function's values at a specific x value. A jump discontinuity can be observed when the graph connects two different points with an open circle.

### Q: How do you determine the limit of a piecewise function?

To determine the limit of a piecewise function, evaluate the left and right limits separately as x approaches a particular value. Compare the left limit and the right limit. If they are equal, the limit exists at that point. If they are not equal, the limit does not exist.

## Summary & Key Takeaways

• The video discusses how to graph piecewise functions by first graphing each part separately and then combining them into a single graph.

• It explains how to identify the domain and range of a piecewise function by considering the allowed x values and the corresponding y values.

• The video also covers how to determine the type of discontinuity in a piecewise function, such as point discontinuity or jump discontinuity.

• It explores how to find the limits of a piecewise function and analyze the left end behavior and right end behavior.