Evaluate the piecewise defined function at the indicated values.
f(x) = 

x2		if x < 0
x + 8	    	if x ≥ 0
f(−4)	 = 	 
f(−3)	 = 	 
f(0)	 = 	 
f(3)	 = 	 
f(4)	 = 	 


The given piecewise function is:

\[
f(x) = 
\begin{cases} 
x^2 & \text{if } x < 0 \\
x + 8 & \text{if } x \geq 0 
\end{cases}
\]

Now let's evaluate \( f(x) \) for the given values:

1. **\( f(-4) \):**
   Since \( -4 < 0 \), we use the first piece of the function: \( f(x) = x^2 \).
   \[
   f(-4) = (-4)^2 = 16
   \]

2. **\( f(-3) \):**
   Since \( -3 < 0 \), we again use the first piece of the function: \( f(x) = x^2 \).
   \[
   f(-3) = (-3)^2 = 9
   \]

3. **\( f(0) \):**
   Since \( 0 \geq 0 \), we use the second piece of the function: \( f(x) = x + 8 \).
   \[
   f(0) = 0 + 8 = 8
   \]

4. **\( f(3) \):**
   Since \( 3 \geq 0 \), we use the second piece of the function: \( f(x) = x + 8 \).
   \[
   f(3) = 3 + 8 = 11
   \]

5. **\( f(4) \):**
   Since \( 4 \geq 0 \), we use the second piece of the function: \( f(x) = x + 8 \).
   \[
   f(4) = 4 + 8 = 12
   \]

### Summary of the values:
\[
f(-4) = 16, \quad f(-3) = 9, \quad f(0) = 8, \quad f(3) = 11, \quad f(4) = 12
\]

Would you like more details on any of the steps or concepts?

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Here are five related questions:
1. What is the domain of this piecewise function?
2. What is the range of this piecewise function?
3. How would you graph this piecewise function?
4. How do you find the derivative of a piecewise function?
5. How can you determine if a piecewise function is continuous?

**Tip:** Always pay attention to the conditions of piecewise functions to choose the correct expression to use.

Evaluate the piecewise defined function at the indicated values. f(x) = x^2 if x < 0; x + 8 if x ≥ 0. f(−4) = ? f(−3) = ? f(0) = ? f(3) = ? f(4) = ?

Explore how to evaluate a piecewise function that switches between a quadratic function (x^2) and a linear function (x + 8) based on the value of x. Learn how to solve for values such as f(-4), f(0), and f(3) with detailed steps. Suitable for students in Grades 9-11.

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