# Graphs of absolute value functions | Functions and their graphs | Algebra II | Khan Academy | Summary and Q&A

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December 19, 2013
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Graphs of absolute value functions | Functions and their graphs | Algebra II | Khan Academy

## TL;DR

Learn how to graph absolute value functions and identify their key features.

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### Q: What is the maximum value of the function f(x)?

The maximum value occurs at x = 1, where f(x) is equal to 9.

### Q: How does the coefficient affect the shape of the graph?

The negative coefficient causes the graph to be downward opening.

### Q: How can the function be divided into two parts?

The function can be divided into one part for x > 1 and another part for x < 1.

### Q: What are the endpoints for the given constrained domain?

The endpoints are f(-4) and f(5), which need to be evaluated to complete the graph.

## Summary & Key Takeaways

• The given absolute value function is f(x) = -3|x - 1| + 9, with a constrained domain of -4 ≤ x ≤ 5.

• The maximum value of the function occurs at x = 1, where f(x) = 9.

• The graph of the function is downward opening due to the negative coefficient.

• The function can be divided into two parts: to the left of the vertex (x < 1) and to the right of the vertex (x > 1).