Answer:
The correct option is C.
Step-by-step explanation:
The general exponential function is
[tex]f(x)=ab^x[/tex]
Where, a is initial value and b is growth factor.
The given function is
[tex]f(x)=(\frac{1}{2})^x[/tex]
Here [tex]b=\frac{1}{2}<1[/tex], therefore it is a decay function. In other words, the given function always decreases.
The given function is defined for all real numbers, therefore the domain of the function is all real number.
Put x=0, to find the y-intercept.
[tex]f(x)=(\frac{1}{2})^0=1[/tex]
The y-intercept of the function is at (0,1). Therefore option C is correct.
[tex](\frac{1}{2})^x>0[/tex]
[tex]f(x)>0[/tex]
Therefore the range of the function is y>0.
