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The function given is \( f(x) = 14(x - 4) \).

This is a linear function because it has the form \( f(x) = mx + b \), which is a straight-line equation. Linear functions have no restrictions on the values of \( x \) that can be used, meaning the domain of the function includes all real numbers.

Now, let’s examine the answer choices:

- A. \( (-\infty, \infty) \): This represents all real numbers, which is correct for a linear function.
- B. \( (-\infty, 0) \cup (0, \infty) \): This excludes \( x = 0 \), which is not a necessary restriction for this function.
- C. \( (-\infty, 0) \cup (0, 4) \cup (4, \infty) \): This excludes \( x = 0 \) and \( x = 4 \), which again is not necessary.
- D. \( (-\infty, 4) \cup (4, \infty) \): This excludes \( x = 4 \), which is not necessary since \( x = 4 \) is valid for this linear function.

Therefore, the correct answer is **A. \( (-\infty, \infty) \)**.

Would you like further explanation or have any questions?

Here are 5 related questions to explore further:
1. How would the domain change if there was a square root in the function?
2. What is the range of a linear function like \( f(x) = 14(x - 4) \)?
3. How do you find the domain of a rational function?
4. What is the effect of including a logarithm in the function for determining the domain?
5. How does a quadratic function's domain compare to that of a linear function?

**Tip:** The domain of a function tells you all the possible input values (values of \( x \)) that will not result in any mathematical contradictions such as division by zero or taking the square root of a negative number.

Find the domain of the function f(x) = 14(x - 4).

Learn how to find the domain of the linear function f(x) = 14(x - 4). Linear functions have no restrictions, so the domain includes all real numbers. This explanation is suitable for students in Grades 7-9.

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