To find the domain and range of the function $f(x) = 8x$, let's break it down:

1. Domain:

The domain of a function consists of all possible values of $x$ that can be input into the function. Since $f(x) = 8x$ is a linear function, there are no restrictions on the values of $x$. This means the function is defined for all real numbers.

Domain: $\mathbb{R}$ (all real numbers) or $(-\infty, \infty)$.

2. Range:

The range of a function is the set of all possible output values $f(x)$. For $f(x) = 8x$, as $x$ takes on all real values, $f(x)$ can also take on all real values. There are no restrictions on the output because a linear function like this can produce any real number.

Range: $\mathbb{R}$ (all real numbers) or $(-\infty, \infty)$.

Summary:

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

Would you like further details or have any questions about this?

Here are some related questions you might find helpful:

1. How would the domain and range change if the function was $f(x) = \frac{1}{x}$?
2. What are the domain and range for a quadratic function like $f(x) = x^2$?
3. How does the domain and range change for a piecewise function?
4. Can the domain and range of a function be restricted by an equation?
5. How do you find the domain and range for a function involving a square root?

Tip: For linear functions like $f(x) = 8x$, the domain and range are always all real numbers unless otherwise restricted by the context of the problem.