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To determine whether the function \( f(x) = 9 - 7x \) is a polynomial function, let's break it down:

### 1. Is \( f(x) \) a polynomial function?
A polynomial function is defined as a function that can be written in the form:

\[
f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0
\]

Where \( a_n, a_{n-1}, \dots, a_0 \) are constants and \( n \) is a non-negative integer. In the given function:

\[
f(x) = 9 - 7x
\]

We can rewrite this as:

\[
f(x) = -7x + 9
\]

This is in the form of a polynomial, where the term \( -7x \) is a linear term (degree 1) and \( 9 \) is a constant (degree 0). Hence, this is a polynomial function.

### 2. What is the degree of the polynomial?
The degree of a polynomial is the highest power of the variable \( x \) in the expression. In \( f(x) = -7x + 9 \), the highest power of \( x \) is 1, so the degree is:

\[
\text{Degree} = 1
\]

### 3. What is the leading coefficient?
The leading coefficient is the coefficient of the term with the highest power of \( x \). In \( f(x) = -7x + 9 \), the term with the highest power of \( x \) is \( -7x \), so the leading coefficient is:

\[
\text{Leading coefficient} = -7
\]

### Conclusion:
- **The function is a polynomial function.**
- The **degree** is **1**.
- The **leading coefficient** is **-7**.

Would you like more details on polynomial functions, or do you have any questions? 

Here are 5 related questions for further exploration:
1. How do you determine whether a function is a polynomial?
2. What are some examples of non-polynomial functions?
3. How do the degree and leading coefficient affect the graph of a polynomial function?
4. What is the difference between a linear polynomial and a quadratic polynomial?
5. How do you find the zeros of a polynomial function?

**Tip:** For polynomial functions, the degree tells you how many times the graph can change direction, and the leading coefficient influences whether the graph opens up or down for higher-degree terms.

Determine whether f(x) = 9 - 7x represents a polynomial function. If it is, state its degree and leading coefficient.

Learn how to determine whether f(x) = 9 - 7x is a polynomial function, and understand how to find its degree and leading coefficient. This problem is suitable for students in Grades 8-10, focusing on key algebra concepts such as polynomial functions and linear equations.

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