Find the range of the function for the given domain. f(x)=4x-8;{-2,-1,0,12}

To find the range of the function \( f(x) = 4x - 8 \) for the given domain \( \{-2, -1, 0, 12\} \), we will calculate \( f(x) \) for each value in the domain.

1. For \( x = -2 \):
   \[
   f(-2) = 4(-2) - 8 = -8 - 8 = -16
   \]

2. For \( x = -1 \):
   \[
   f(-1) = 4(-1) - 8 = -4 - 8 = -12
   \]

3. For \( x = 0 \):
   \[
   f(0) = 4(0) - 8 = 0 - 8 = -8
   \]

4. For \( x = 12 \):
   \[
   f(12) = 4(12) - 8 = 48 - 8 = 40
   \]

Now we can list the output values:
- \( f(-2) = -16 \)
- \( f(-1) = -12 \)
- \( f(0) = -8 \)
- \( f(12) = 40 \)

Thus, the range of the function \( f(x) \) for the given domain is:
\[
\{-16, -12, -8, 40\}
\]

### Summary
- **Function**: \( f(x) = 4x - 8 \)
- **Domain**: \( \{-2, -1, 0, 12\} \)
- **Range**: \( \{-16, -12, -8, 40\} \)

Would you like further details or have any questions? Here are some related questions you might consider:

1. How would the range change if the domain were different?
2. What is the slope and intercept of the function \( f(x) \)?
3. Can you find the inverse of the function \( f(x) \)?
4. How do you graph the function \( f(x) \)?
5. What would the range be if the function was transformed, say by adding a constant? 

**Tip**: Always evaluate functions at each point in the domain to find the corresponding outputs for determining the range.

Explore how to find the range of the function f(x) = 4x - 8 for the specific domain {-2, -1, 0, 12}. The solution details calculations and outputs, leading to the range of {-16, -12, -8, 40}. Ideal for students in Grades 7-9.

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