Answer :
To solve the problem regarding the function [tex]\( f(x) = 5x^3 + 2 \)[/tex], we need to identify three aspects: the leading coefficient, the type of the function, and the name of the function.
1. Leading Coefficient:
The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. In the function [tex]\( f(x) = 5x^3 + 2 \)[/tex], the term with the highest degree is [tex]\( 5x^3 \)[/tex]. Here, the leading coefficient is 5.
2. Type:
The type of a function can be classified based on its highest degree. The highest degree here is 3, which indicates that this function is a type of polynomial function. Therefore, the type of this function is polynomial.
3. Name:
The name of a polynomial function is also determined by its degree. A polynomial with a degree of 3 is specifically known as a cubic polynomial.
Putting it all together, we have the following for the function [tex]\( f(x) = 5x^3 + 2 \)[/tex]:
- The leading coefficient is 5.
- The type of the function is polynomial.
- The name of the function is cubic.
1. Leading Coefficient:
The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. In the function [tex]\( f(x) = 5x^3 + 2 \)[/tex], the term with the highest degree is [tex]\( 5x^3 \)[/tex]. Here, the leading coefficient is 5.
2. Type:
The type of a function can be classified based on its highest degree. The highest degree here is 3, which indicates that this function is a type of polynomial function. Therefore, the type of this function is polynomial.
3. Name:
The name of a polynomial function is also determined by its degree. A polynomial with a degree of 3 is specifically known as a cubic polynomial.
Putting it all together, we have the following for the function [tex]\( f(x) = 5x^3 + 2 \)[/tex]:
- The leading coefficient is 5.
- The type of the function is polynomial.
- The name of the function is cubic.
