Question

Which statements accurately describe the function f(x) = 3(16)^3/4? Check all that apply.

The initial value is 3.
The initial value is 48.
The domain is x > 0.
The range is y >0.
The simplified base is 12.
The simplified base is 8.

Answer 1

a,c,e

Step-by-step explanation:

Answer 2

Answers:

These are the statements that apply:

The initial value is 3.

The range is y >0.

The simplified base is 8.

Step-by-step explanation:

1) Given expression:

`f(x)=3(16)^{(3)/(4) x`

2) Check every statement:

a) The initial value is 3?

initial value ⇒ x = 0 ⇒

`f(0)=3(16)^(0)=3(1)=3`

∴ The statement is right.

b) The initial value is 48?

Not, as it was already proved that it is 3.

c) The domain is x > 0?

No, because the domain of the exponential functions is all the Real numbers.

d) The range is y > 0?

That is correct, the exponential function is continuous, and monotonon increasing.

The limit when x → - ∞ is zero, but y never reaches zero, and the limit when x → ∞ is + ∞, meaning that the range is y > 0.

e) The simplified base is 12?

This is how you simplify the base:

`3(16)^{(3)/(4) x}=3{{(16}^((3/4)))}^x=3(16^(3/4)})^(x)=3((2^4)^(3/4))^x=3(2^3)^x=3(8)^x`

Which shows that the simplified base is 8 (not 12).

f) The simplified base is 8?

Yes; this was just proved.