State the domain of the graph of f(x) = -2x + 3.



The function \( f(x) = -2x + 3 \) is a linear function. Since there are no restrictions on \( x \) (such as square roots, logarithms, or denominators that could make the function undefined), the domain of this function includes all real numbers.

Thus, the domain of \( f(x) \) is:

\[
\boxed{(-\infty, \infty)}
\]

Would you like further details on graphing linear functions or any related concepts?

Here are five related questions:
1. What is the range of the function \( f(x) = -2x + 3 \)?
2. How does the slope of \( f(x) = -2x + 3 \) affect the graph's steepness?
3. What is the \( y \)-intercept of \( f(x) = -2x + 3 \)?
4. How do you find the \( x \)-intercept of a linear function?
5. How does the graph of \( f(x) = -2x + 3 \) compare to \( f(x) = 2x + 3 \)?

**Tip:** For linear functions of the form \( f(x) = mx + b \), the domain is always all real numbers, unless restrictions are explicitly given.

State the domain of the graph of f(x) = -2x + 3.

Learn how to find the domain of the linear function f(x) = -2x + 3 with this detailed solution. This problem explains key algebraic concepts, such as the domain of linear functions, using the formula f(x) = mx + b. Ideal for students in Grades 7-9.

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