Question

Simplify the function f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction. Then determine the key aspects of the function. The initial value is . The simplified base is . The domain is . The range is .

Answer 1

Answer:

The answer is given below

Step-by-step explanation:

Given that:

$f(x)=\frac{1}{3}(81)^ \frac{3x}{4} \\Using\ exponent\ rule:a^{xy}=a^xa^y\\f(x)=\frac{1}{3}(81^{1/4})^ {3x}\\f(x)=\frac{1}{3}(3})^ {3x}\\f(x)=\frac{(3)^ {3x}}{3^1} \\Using\ exponent\ rule:a^x/a^y=a^{x-y}\\f(x)=3^ {3x-1}$

The function is an exponential function.

The domain is the set of all independent variables i.e the input values (x values). For an exponential function, the domain is the set of all real numbers. That is:

Domain: x = (-∞, ∞)

The range is the set of all dependent variables i.e the values of y. For an exponential function, the range is the set of all real numbers greater than zero. That is:

Range: y = (0, ∞)

Answer 2

Answer:

initial value 1/3

simplified base 27

domain is all real numbers

range is y>0

Step-by-step explanation: