What is the natural domain for f(x) = 7 - 3x

The natural domain of the function \( f(x) = 7 - 3x \) includes all real values of \( x \) for which the function is defined. Since this function is a linear expression with no restrictions such as square roots, logarithms, or divisions by zero, \( f(x) \) is defined for all real numbers.

Therefore, the natural domain of \( f(x) = 7 - 3x \) is:

\[
(-\infty, \infty)
\]

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Here are five related questions that explore similar concepts:

1. What is the natural domain of \( g(x) = \frac{5}{x - 2} \)?
2. How do you find the domain of \( h(x) = \sqrt{5 - x} \)?
3. What is the domain of \( k(x) = \ln(x + 1) \)?
4. If \( f(x) = 7 - 3x \), what is its range?
5. How would you determine the domain of a quadratic function, such as \( f(x) = x^2 - 4x + 4 \)?

**Tip:** For functions with square roots, logarithms, or fractions, look out for domain restrictions where inputs can lead to undefined or non-real values.

What is the natural domain for f(x) = 7 - 3x?

Understand how to find the natural domain of the linear function f(x) = 7 - 3x. This solution covers the basic algebraic concept of a function's domain, demonstrating that linear functions are defined for all real numbers. Suitable for students in Grades 7-9.

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