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.

Explore how to find the domain and range of the linear function f(x) = 8x. This problem covers fundamental algebraic concepts such as linear functions, and explains why the domain and range are both all real numbers. Ideal for students in Grades 9-10.

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