Question

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).
( f(x)=2 x^{4}-12 x^{2} )
what is the domain of the function?
the domain is ( (-infty, infty) ).
(type your answer in interval notation. use a comma to separate answers as needed.)
what is the ( y )-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the ( y )-intercept is ( y = 0 ).
b. there is no ( y )-intercept.
what is/are the ( x )-intercept(s)? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the ( x )-intercept(s) is/are ( x = )
(type an exact answer, using radicals as needed. use a comma to separate answers as needed.)
b. there is no ( x )-intercept.

Explanation:

Step1: Find the x - intercepts

Set \(y = f(x)=0\), so \(2x^{4}-12x^{2}=0\). Factor out \(2x^{2}\): \(2x^{2}(x^{2}-6)=0\).
Using the zero - product property \(a\times b = 0\) implies \(a = 0\) or \(b = 0\).
For \(2x^{2}=0\), we get \(x = 0\).
For \(x^{2}-6=0\), we have \(x^{2}=6\), then \(x=\pm\sqrt{6}\).

Answer:

A. The \(x\) - intercept(s) is/are \(x =-\sqrt{6},0,\sqrt{6}\)