https://file.aiquickdraw.com/mathbot/file/1726871338829dpye2374.jpg

The question in your image asks: *"What value should be assigned to \( f(2) \) to make the extended function continuous at \( x = 2 \)?"*

From the right-hand side, it looks like the function is piecewise, with different expressions depending on the value of \( x \). To make the function continuous at \( x = 2 \), the left-hand limit and right-hand limit as \( x \) approaches 2 must be equal, and the function value at \( x = 2 \) must match these limits.

Could you provide a closer view or describe the piecewise function? This will help in determining the appropriate value for \( f(2) \) to ensure continuity.

Let me know if you'd like me to elaborate further or explain any concepts!

Here are some relative questions to consider:
1. What is the definition of continuity for a function at a point?
2. How do you calculate the left-hand and right-hand limits of a function?
3. What are piecewise functions and how do they affect continuity?
4. Can a function be continuous if it has a hole or jump at a specific point?
5. How do you use limits to determine if a function is continuous?

**Tip:** Continuity at a point implies that the function's limit from both sides and the function's value at that point must all be equal.

What value should be assigned to f(2) to make the extended function continuous at x = 2?

Learn how to determine the value of f(2) to make a piecewise function continuous at x = 2. This problem covers limits and continuity concepts, focusing on piecewise-defined functions and their behavior at a specific point. Suitable for students in Grades 11-12 and college-level courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation