To determine the function type represented by the given equation, let's analyze it step-by-step.
Given the equation:
[tex]\[
f(x) = 0.005 \left(x^3 - 15x^2 - 325x + 1875\right)
\][/tex]
1. Identify the polynomial:
The term inside the parentheses [tex]\((x^3 - 15x^2 - 325x + 1875)\)[/tex] is a polynomial.
2. Determine the highest power of [tex]\( x \)[/tex]:
In the polynomial given, the highest power of [tex]\( x \)[/tex] is [tex]\( x^3 \)[/tex]. This tells us the degree of the polynomial.
3. Classification by degree:
Polynomial functions are named based on their degree, which is the highest power of [tex]\( x \)[/tex] in the equation:
- A polynomial of degree 1 is called a linear polynomial.
- A polynomial of degree 2 is called a quadratic polynomial.
- A polynomial of degree 3 is called a cubic polynomial.
Since the highest power of [tex]\( x \)[/tex] in our polynomial is [tex]\( x^3 \)[/tex], the degree of the polynomial is 3.
4. Function type:
A polynomial with a degree of 3 is known as a cubic polynomial.
Therefore, the given equation represents a cubic polynomial function. This conclusion is based on identifying the highest power term in the polynomial, indicating that it is of the third degree.
