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------------------------------------------------ Consider the function [tex]f(x) = 5x^3 + 2[/tex].

19. Leading coefficient: [tex]\qquad[/tex]

20. Type: [tex]\qquad[/tex]

21. Name: [tex]\qquad[/tex]

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.