Find all values of x for which the given function is continuous.
f (x) = 2x

The given function is \( f(x) = 2x \). This is a linear function, which means it is continuous for all real values of \( x \).

### Explanation:
- Linear functions have the general form \( f(x) = ax + b \), where \( a \) and \( b \) are constants.
- Such functions are continuous everywhere because there are no breaks, jumps, or holes in their graphs.

Thus, \( f(x) = 2x \) is continuous for **all real numbers**.

### Conclusion:
The function \( f(x) = 2x \) is continuous for all values of \( x \in (-\infty, \infty) \).

Would you like more details, or do you have any questions?

Here are 5 related questions you might explore:
1. What is the definition of continuity for a function?
2. Are all polynomial functions continuous?
3. How do we determine the continuity of a piecewise function?
4. What are some examples of discontinuous functions?
5. Can a function be continuous but not differentiable?

**Tip:** A function is continuous at a point if the limit from both sides equals the function value at that point.

Find all values of x for which the given function is continuous. f(x) = 2x

Explore the continuity of the linear function f(x) = 2x. Learn how linear functions, represented by the formula f(x) = ax + b, are continuous for all real numbers. This concept is essential in understanding continuity in algebra and calculus, suitable for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation