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} )
a the domain of ( f ) is ( (-infty, infty) ).
(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.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a the ( x )-intercept(s) of ( f ) is/are ( x = 0, \frac{9}{4} ).
(type an exact answer, using radicals as needed. type an integer or a fraction. use a comma to separate answers as needed)
b the function ( f ) has no ( x )-intercepts
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a the ( y )-intercept of ( f ) is ( y = )
(type an exact answer, using radicals as needed. use a comma to separate answers as needed)
b. the function ( f ) has no ( y )-intercept

Explanation:

Step1: Find the y - intercept

To find the y - intercept, we set \(x = 0\) in the function \(y=f(x)=4x^{6}-9x^{5}\).
Substitute \(x = 0\) into the function: \(y=4\times0^{6}-9\times0^{5}=0\)

Answer:

A. The y - intercept of \(f\) is \(y = 0\)