is it true or false that f(x)=2√x has the same domain and range as f(x)=√x

Answer 1

Hello Taylor,

In general, when you have a vertical transformation of the type c*f(x), for c>0, the domain of the function doesn't change at all. Notice that 2sqrt(x) is a vertical transformation of sqrt(x), so they should have the same domain.

Best,

Answer 2

Yes because the driving function is the same.

Both domains and ranges are x>=0 or (0, infinity)

the only difference is that one will approach infinity faster than the other