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The given function is \( f(x) = 4x^2 + 7x^3 \).

### Determining if it is a polynomial:
A polynomial function is an expression that consists of terms made up of constants and variables raised to non-negative integer powers. In this case, both terms \( 4x^2 \) and \( 7x^3 \) meet these criteria because:
- \( 4x^2 \) has the variable \( x \) raised to the power of 2 (a non-negative integer).
- \( 7x^3 \) has the variable \( x \) raised to the power of 3 (a non-negative integer).

Thus, **this is a polynomial function**.

### Identifying the degree:
The degree of a polynomial is the highest power of the variable \( x \). In this case, the highest exponent is 3 (from the term \( 7x^3 \)). Therefore, the degree of the polynomial is **3**.

### Answer:
- **Option A**: It is a polynomial. The degree of the polynomial is **3**.

Do you want more details or have any questions?

Here are five related questions:
1. What are the conditions for a function to be classified as a polynomial?
2. Can polynomial functions have negative or fractional exponents?
3. How do you find the degree of more complex polynomials?
4. What is the role of the leading coefficient in a polynomial?
5. How do you graph a polynomial function based on its degree?

**Tip:** Always look at the highest exponent to quickly determine the degree of a polynomial function.

Determine whether the function is a polynomial function. If it is, identify the degree. f(x) = 4x^2 + 7x^3

This problem explores how to determine if a given function, f(x) = 4x^2 + 7x^3, is a polynomial. Learn the steps to identify the degree of a polynomial, and apply this to algebraic functions. Suitable for students in Grades 9-12.

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