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.