https://r2.erweima.ai/mathbot/image/1725471901147esfbxu90.jpg


Find a formula for the function graphed.

The graph provided shows a piecewise function consisting of two horizontal line segments. Let’s analyze each segment individually.

1. **First Segment:**
   - This segment is horizontal, indicating a constant function.
   - The segment extends from \( x = -4 \) to \( x = -1 \), with a constant \( y \)-value of \( y = -2 \).
   - Therefore, for this interval, the function is:
     \[
     f(x) = -2 \quad \text{for } -4 \leq x \leq -1
     \]

2. **Second Segment:**
   - This segment is also horizontal, indicating another constant function.
   - The segment extends from \( x = 0 \) to \( x = 4 \), with a constant \( y \)-value of \( y = 1 \).
   - Therefore, for this interval, the function is:
     \[
     f(x) = 1 \quad \text{for } 0 \leq x \leq 4
     \]

Given this analysis, the piecewise function \( f(x) \) represented by the graph is:

\[
f(x) =
\begin{cases} 
-2 & \text{if } -4 \leq x \leq -1 \\
1 & \text{if } 0 \leq x \leq 4 
\end{cases}
\]

Would you like more details on this, or do you have any questions? Here are some related questions you might find helpful:

1. How do you determine the equation of a horizontal line?
2. What would the function look like if there were more segments?
3. How do we express a function with more complex shapes, such as curves?
4. What are the key differences between continuous and piecewise functions?
5. How do you graph a piecewise function from its formula?

**Tip:** When working with piecewise functions, pay careful attention to the domain of each piece to ensure that the overall function is correctly defined for all intervals.

Discover how to find a formula for a piecewise function from a graph. This problem involves analyzing horizontal line segments and defining the function in intervals. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation