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Please answer the question or the questions

We are given the function \( k(x) \) defined piecewise as follows:

\[
k(x) = 
\begin{cases} 
4 & \text{if } x < 0 \\
x + 8 & \text{if } 0 \leq x < 1 \\
1 - x & \text{if } x \geq 1 
\end{cases}
\]

Let's evaluate the given points:

### (a) \( k(-4) \)
Since \( -4 < 0 \), we use the first part of the piecewise function:

\[
k(-4) = 4
\]

### (b) \( k(0) \)
Since \( 0 \leq 0 < 1 \), we use the second part of the piecewise function:

\[
k(0) = 0 + 8 = 8
\]

### (c) \( k(1) \)
Since \( 1 \geq 1 \), we use the third part of the piecewise function:

\[
k(1) = 1 - 1 = 0
\]

### (d) \( k(-0.009) \)
Since \( -0.009 < 0 \), we use the first part of the piecewise function:

\[
k(-0.009) = 4
\]

### Summary of answers:
- (a) \( k(-4) = 4 \)
- (b) \( k(0) = 8 \)
- (c) \( k(1) = 0 \)
- (d) \( k(-0.009) = 4 \)

Would you like any more details or clarifications on these steps?

Here are some follow-up questions:
1. What is a piecewise function, and how do you identify which part to use?
2. How would the function behave for values like \( x = 2 \)?
3. Can you explain how the function behaves at the boundaries \( x = 0 \) and \( x = 1 \)?
4. What happens if \( x \) is a decimal between 0 and 1?
5. How does the third part of the piecewise function behave for very large values of \( x \)?

**Tip:** When dealing with piecewise functions, always check the domain for each condition to select the correct piece to evaluate.

If k(x) is a piecewise function defined as follows: k(x) = 4 if x < 0, k(x) = x + 8 if 0 ≤ x < 1, and k(x) = 1 - x if x ≥ 1. Find k(-4), k(0), k(1), and k(-0.009).

Learn how to evaluate a piecewise function for different values of x, including negative and boundary points. This problem covers piecewise function definitions and evaluations, suitable for students in Grades 10-12.

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