Question

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 .

Answer 1

A, C , E

Explanation:

Answer 2

The domain is all real numbers.

The initial value is 3

The simplified base is
`9√(2)`

Explanation:

The given function is
`f(x)=3(√(18))^x`.

To find the initial value, we put x=0 into the function:

`f(0)=3(√(18))^0`.

`f(0)=3(1)=3`.

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
`y\:>\:0`

The simplified base is
`3√(18)=3√(9*2)`.

`3√(18)=3√(9)*√(2)`

`3√(18)=3*3*√(2)`

`3√(18)=9√(2)`