Question

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).
( f(x)=4 x^{6}-9 x^{5} )
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the domain of ( f ) is
(type your answer in interval notation. type an exact answer, using radicals as needed. use a comma to separate answers as needed)
b. the domain of ( f ) is empty.

Explanation:

Step1: Analyze the function type

The function \( f(x)=4x^{6}-9x^{5}\) is a polynomial function.

Step2: Determine the domain of polynomial functions

For any polynomial function \(y = a_nx^n+\cdots+a_1x + a_0\) (\(n\) is a non - negative integer and \(a_i\in R\)), the domain is all real numbers. In interval notation, the set of all real numbers is \((-\infty,\infty)\)

Answer:

A. The domain of \(f\) is \((-\infty,\infty)\)