Question

consider the function f(x)= (1/2)(picture of graph below) - function f has a domain of ___( x<0 | x>0 | all real numbers)and the range of ___( y>0 | y<0| all real numbers) . the function ______( approaches negative infinity | approaches y=0 | approaches positive infinity) as x increases)

Answer 1

$\begin{gathered} \text{Given} \\ f(x)=(\frac{1}{2})^x \end{gathered}$

Seeing that the given function is exponential, there are no restrictions to its domain therefore, the domain of the function is all real numbers.

Since the coefficient of the exponential function is positive and there are no constants, then range of the function is y > 0.

Since the base of the function is less than 1, in this case (1/2), then as x increases y approaches 0.