How do you find the domain and range of #f(x)=sqrt(5x+1)#?
Domain is pretty easy. It just takes some logic: we cannot take a square root of a negative number, so
With that in mind, we just need to set the expression inside the square root equal to
We include the
Now on to the range. This one is also pretty easy. We just need to see if there are any additions or subtractions outside of the square root. Those would be vertical shifts, and are responsible for changes in the range.
In our case, there are no vertical shifts, so the range is the same as the parent graph
Let's graph our equation and see if we're right
We are. The graph begins at