f(x)=ax⇒f′(x)=axlna.
For f to be increasing on R, f′(x)>0 for all x.
Since ax>0 for a>0, we need lna>0, i.e., a>1.
Note: We have selected option (3) based on the strict mathematical definition of increasing. The original key marks (1), but for 0<a<1 the function is decreasing, so 1<a<∞ is the correct range.