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)=2 x^{4}-12 x^{2} )\nwhat is the domain of the function?\nthe domain is ( (-infty, infty) ).\n(type your answer in interval notation. use a comma to separate answers as needed.)\nwhat is the ( y )-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( y )-intercept is ( y = 0 ).\nb. there is no ( y )-intercept.\nwhat is/are the ( x )-intercept(s)? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) is/are ( x = ) \n(type an exact answer, using radicals as needed. use a comma to separate answers as needed.)\nb. there is no ( x )-intercept.

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

Answer

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})