https://file.aiquickdraw.com/mathbot/file/17255968432397hlovd1s.jpg

In the image you provided, the graph shows a piecewise function consisting of three distinct sections. We need to describe the piecewise function \( f(x) \) based on the given graph.

### Analyzing the graph:
1. **First interval** (for \( x < -3 \)): There is a horizontal line at \( y = -3 \) between \( x = -6 \) and \( x = -3 \), excluding \( x = -3 \).
2. **Second interval** (for \( -3 \leq x < 2 \)): There is a horizontal line at \( y = 2 \) between \( x = -3 \) and \( x = 2 \), including \( x = -3 \) but excluding \( x = 2 \).
3. **Third interval** (for \( x \geq 2 \)): There is a horizontal line at \( y = 4 \) starting at \( x = 2 \) and continuing for larger values of \( x \), including \( x = 2 \).

### Writing the piecewise function:
We can describe this as:
\[
f(x) =
\begin{cases} 
-3 & \text{if } x < -3, \\
2  & \text{if } -3 \leq x < 2, \\
4  & \text{if } x \geq 2.
\end{cases}
\]

### Explanation of each interval:
- For \( x < -3 \), the graph is at \( y = -3 \), and the function excludes \( x = -3 \) (open circle at \( x = -3 \)).
- For \( -3 \leq x < 2 \), the graph is at \( y = 2 \), and the function includes \( x = -3 \) (closed circle) but excludes \( x = 2 \) (open circle at \( x = 2 \)).
- For \( x \geq 2 \), the graph is at \( y = 4 \), and the function includes \( x = 2 \) (closed circle) and continues for all \( x > 2 \).

Would you like further details or clarifications?

Here are 5 related questions to expand on this:
1. How would you write the piecewise function if the intervals were non-continuous?
2. Can piecewise functions have non-constant expressions for each interval?
3. How do you determine whether to include or exclude endpoints in piecewise functions?
4. How does the graph of a piecewise function change if the intervals overlap?
5. What real-life situations can be modeled using piecewise functions?

**Tip:** When working with piecewise functions, carefully note whether each endpoint is included or excluded by looking at the open or closed circles on the graph.

Complete the description of the piecewise function graphed below.

Learn how to describe a piecewise function from a graph using intervals. This problem covers essential algebraic concepts, including piecewise functions, function notation, and how to handle inclusion and exclusion of endpoints. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation