https://file.aiquickdraw.com/mathbot/file/17259329586243iuiqh6s.jpg

Let's analyze the given piecewise function \( f(x) \) and calculate the required values.

The function is defined as:
\[
f(x) = \begin{cases} 
x - 7 & \text{if } x \leq 3 \\
3 - x & \text{if } x > 3 
\end{cases}
\]

We need to calculate:
1. \( f(-4) \)
2. \( f(3) \)
3. \( f(8) \)

### 1. \( f(-4) \)
Since \( -4 \leq 3 \), we use the first part of the piecewise function:
\[
f(-4) = -4 - 7 = -11
\]

### 2. \( f(3) \)
Since \( 3 \leq 3 \), we use the first part of the piecewise function again:
\[
f(3) = 3 - 7 = -4
\]

### 3. \( f(8) \)
Since \( 8 > 3 \), we use the second part of the piecewise function:
\[
f(8) = 3 - 8 = -5
\]

### Final Answers:
\[
f(-4) = -11, \quad f(3) = -4, \quad f(8) = -5
\]

Would you like more details on this? Here are 5 related questions that might help expand your understanding:

1. How do we determine which part of the piecewise function to use?
2. What is a piecewise function, and why is it useful?
3. What happens when \( f(x) \) has more than two pieces?
4. Can you plot a graph of this piecewise function to visualize it?
5. How would the function change if we modified the conditions (e.g., changing \( x \leq 3 \) to \( x < 3 \))?

**Tip:** When working with piecewise functions, always pay close attention to the boundary values of each condition to choose the correct formula!

Find the values of f(-4), f(3), and f(8) for the piecewise function f(x) = {x - 7 if x ≤ 3, 3 - x if x > 3}.

Find the values of the piecewise function f(x) = {x - 7 if x ≤ 3, 3 - x if x > 3} at x = -4, x = 3, and x = 8. A detailed explanation of each step is provided, showing how to handle piecewise functions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation