summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y =…

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).\n( f(x) = 4x^{6}-9x^{5} )\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the domain of ( f ) is ( (-infty,infty) ).\n(type your answer in interval notation. type an exact answer, using radicals as needed. use a comma to separate answers as needed.)\nb. the domain of ( f ) is empty.\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) of ( f ) is/are ( x = ).\n(type an exact answer, using radicals as needed. type an integer or a fractic. use a comma to separate answers as needed.)\nb. the function ( f ) has no ( x )-intercepts.

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).\n( f(x) = 4x^{6}-9x^{5} )\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the domain of ( f ) is ( (-infty,infty) ).\n(type your answer in interval notation. type an exact answer, using radicals as needed. use a comma to separate answers as needed.)\nb. the domain of ( f ) is empty.\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) of ( f ) is/are ( x = ).\n(type an exact answer, using radicals as needed. type an integer or a fractic. use a comma to separate answers as needed.)\nb. the function ( f ) has no ( x )-intercepts.

Answer

Explanation:

Step1: Find the x - intercepts

Set (y = f(x)=0), so (4x^{6}-9x^{5}=0). Factor out (x^{5}): (x^{5}(4x - 9)=0).

Step2: Solve the equation

Using the zero - product property (ab = 0) implies (a = 0) or (b = 0). If (x^{5}=0), then (x = 0). If (4x-9=0), then (4x=9), and (x=\frac{9}{4}).

Answer:

A. The (x) - intercept(s) of (f) is/are (x = 0,\frac{9}{4})