Answer:
The domain is all real numbers.
The initial value is 3
The 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]
