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.

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

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.

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

• 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).