Graphs of absolute value functions | Functions and their graphs | Algebra II | Khan Academy | Summary and Q&A
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TL;DR
Learn how to graph absolute value functions and identify their key features.
Key Insights
- 🟰 The maximum value of an absolute value function occurs when the absolute value part equals 0.
- 😥 The vertex of an absolute value function represents its maximum or minimum point and is integral to graphing it accurately.
- ☠️ The slope of an absolute value function determines its direction and rate of change.
- 🥳 Dividing the function into parts based on the vertex helps simplify the graphing process.
Transcript
Let's think a little bit about the graphs of absolute value functions. And I've defined one right over here. f of x is equal to negative 3 times the absolute value of x minus 1 plus 9. And then we've constrained its domain. This is for x being-- or negative 4 is less than or equal to x, which is less than or equal to 5. And I encourage you to pause... Read More
Questions & Answers
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
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The given absolute value function is f(x) = -3|x - 1| + 9, with a constrained domain of -4 ≤ x ≤ 5.
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The maximum value of the function occurs at x = 1, where f(x) = 9.
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The graph of the function is downward opening due to the negative coefficient.
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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).
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