If the function passes through the origin, when x is equal to zero y must be equal to zero.
Replacing x=0 in the functions, we have:
Power function
y=(0)^n=0
We see that the power function must pass through the origin.
Root function
y=(0)^(1/n)=0
We see that the root function must pass through the origin.
Reciprocal function
y=1/0 = undefined
We see that the reciprocal function does not pass through the origin.
Exponential function
y=b^0=1
We see that the exponential function does not pass through the origin.
The answers are the options A and B.