The problem is asking the x values for which f(x) is discontinuous 

To determine the \( x \)-values for which the function \( f(x) \) is discontinuous, we need to identify points on the graph where there is a break, jump, or any other kind of interruption in the curve.

From the graph you provided, it appears there are two distinct discontinuities. Discontinuities typically occur at:

1. **Jumps:** Where the function suddenly "jumps" from one value to another.
2. **Asymptotes:** Where the function approaches infinity or negative infinity.
3. **Holes:** Points where the function is undefined or not connected.

**From the graph, the discontinuities seem to occur at the following \( x \)-values:**

- **At \( x = -3 \)**: There seems to be a jump discontinuity. The graph breaks and jumps from one point to another at this value.
- **At \( x = 1 \)**: There seems to be another discontinuity. The curve has a break or sudden change in direction at this value.

So, the function \( f(x) \) is discontinuous at \( x = -3 \) and \( x = 1 \).

Would you like further explanation on this or have any other questions? Here are some related questions you might consider:

1. What are the types of discontinuities?
2. How do we mathematically define a jump discontinuity?
3. What conditions must be met for a function to be continuous at a point?
4. How can we find discontinuities algebraically?
5. Can a function have an infinite number of discontinuities?

**Tip:** When analyzing a graph for discontinuities, always check for breaks, jumps, and undefined points.

Discover how to identify discontinuities in functions and determine the x values where f(x) is discontinuous. This problem explores key concepts such as jumps, asymptotes, and holes, crucial for understanding function behavior. Suitable for advanced high school 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