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Part 1

Find the domain of the function.

f left parenthesis x right parenthesis equals 9 left parenthesis x plus 11 right parenthesis

The function given is:

\[
f(x) = 9(x + 11)
\]

### Step 1: Analyze the function structure
The function is a linear function, which means it is a polynomial of degree 1. Polynomials are continuous and defined for all real numbers because they do not involve any restrictions like division by zero or taking square roots of negative numbers.

### Step 2: State the domain
Since the function \( f(x) = 9(x + 11) \) is a linear polynomial, it is defined for all real values of \(x\). Thus, the domain is:

\[
\text{Domain of } f(x) = (-\infty, \infty)
\]

Would you like further details on any specific part?

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Here are 5 related questions to explore:

1. What is the range of a linear function?
2. How would the domain change if there were a square root in the function?
3. How do you find the domain of a rational function?
4. How does the domain of a logarithmic function differ from that of a polynomial?
5. What happens to the domain if the function involves a denominator?

**Tip:** When analyzing the domain of a function, always look for operations like division or square roots, as they often impose restrictions.

Find the domain of the function. f(x) = 9(x + 11)

Learn how to find the domain of the linear function f(x) = 9(x + 11). This problem covers important algebraic concepts related to linear functions and their domains. Suitable for students in Grades 6-8.

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