Which statements accurately describe the function f(x) = 3(StartRoot 18 EndRoot) Superscript x? Select three options. The domain is all real numbers. The range is y > 3. The initial value is 3. The initial value is 9. The simplified base is .
Accepted Solution
A:
Answer:The domain is all real numbers.The initial value is 3The simplified base is [tex]9\sqrt{2}[/tex]Step-by-step explanation:The given function is [tex]f(x)=3(\sqrt{18})^x[/tex].To find the initial value, we put x=0 into the function: [tex]f(0)=3(\sqrt{18})^0[/tex].[tex]f(0)=3(1)=3[/tex].The initial value is actually 3.The given function is an exponential function, therefore the domain is all real numbers.The range of this function refers to all values of y for which the function is defined.The line y=0, is the horizontal asymptote. The range is [tex]y\:>\:0[/tex]The simplified base is [tex]3\sqrt{18}=3\sqrt{9\times2}[/tex].[tex]3\sqrt{18}=3\sqrt{9}\times\sqrt{2}[/tex][tex]3\sqrt{18}=3\times3\times\sqrt{2}[/tex][tex]3\sqrt{18}=9\sqrt{2}[/tex]