Question

How do you describe the transformation of `f(x)=sqrt(3x)+1` from a common function that occurs and sketch the graph?

Answer 1

The "`+1`" term indicates the function will be "up `1`" relative to the base function.

The "`sqrt(3x)`" term indicates that the function has a horizontal "shrink factor" of `1/3` compared to the base `sqrtx`.

The graph of the parent function, `f(x) = sqrtx`:

graph{sqrtx [-9.045, 10.955, -5.68, 4.32]}

And the graph of `f(x) = sqrt(3x) + 1`:

graph{sqrt(3x) + 1 [-6.88, 13.12, -5.04, 4.96]}