The function you provided is $f(x) = -x$, which is a linear function with a slope of -1. Let's go through the steps to find its domain and range.

Domain:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function $f(x) = -x$, there are no restrictions on $x$—you can input any real number. Thus, the domain is:

$\boxed{\mathbb{R}} \quad \text{(all real numbers)}$

Range:

The range of a function is the set of all possible output values (y-values). Since the function is linear and spans all real numbers, for every input $x$, there is a corresponding output $y = -x$. This means the function can take any real value for $y$. Therefore, the range is also:

$\boxed{\mathbb{R}} \quad \text{(all real numbers)}$

Summary:

• Domain: $\mathbb{R}$ (all real numbers)
• Range: $\mathbb{R}$ (all real numbers)

Would you like more details on linear functions or the properties of the graph? Or do you have any other questions?

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Here are 5 related questions you might find interesting:

1. How does the slope of a linear function affect the graph's domain and range?
2. What happens to the domain and range of a function if it is quadratic instead of linear?
3. How do you find the domain and range for piecewise functions?
4. Can a function have a restricted domain or range? If so, how?
5. What are some examples of functions with specific domains and ranges, like exponential or trigonometric functions?

Tip: Remember, for any linear function like $f(x) = mx + b$, the domain and range are both typically $\mathbb{R}$, unless specific constraints are imposed.