Use the given domain to find the range of each function. f(x) = |x|, D = {-4, 0, -3} R = {,,}

To find the range of the function \( f(x) = |x| \) for the given domain \( D = \{-4, 0, -3\} \), we evaluate the function at each point in the domain:

1. \( f(-4) = |-4| = 4 \)
2. \( f(0) = |0| = 0 \)
3. \( f(-3) = |-3| = 3 \)

Thus, the range \( R \) is the set of outputs from these calculations:

\[
R = \{4, 0, 3\}
\]

If you have any questions or want further details, feel free to ask!

Here are five related questions:
1. What is the range if the domain was \( \{-5, -2, 2\} \)?
2. How does the function \( f(x) = |x| \) change if the domain includes positive numbers?
3. Can the range of \( f(x) = |x| \) ever include negative numbers?
4. How would the range change if the function was \( f(x) = -|x| \)?
5. What is the range if the domain was \( \{-4, 4, -3, 3\} \)?

**Tip:** The range of the absolute value function is always non-negative because absolute values represent the distance from zero.

Explore how to find the range of the absolute value function f(x) = |x| for the domain D = {-4, 0, -3}. Learn step-by-step how to calculate the absolute values and determine the corresponding range R = {4, 0, 3}. Suitable for middle school students learning about functions and absolute values.

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