describe how the graph of `g(x)=root(3)(x-6)` can be obtained from the graph of `root(3)(x)` then graph the function g(x).
Given a base function `f(x)` , there are a number of transformations that can be applied to get a new function. If `g(x)=Af(B(x-h))+k` then g(x) is a transformation of f(x). The transformations include:
A: A creates a vertical stretch/compression of size A. Also, if A<0 the function is reflected over the x-axis.
B: B creates a horizontal stretch/compression. Usually this is most noticeable in periodic functions such as the trigonometric functions. In typical algebraic functions, horizontal stretch/compressions can be seen as vertical stretch/compressions. If B<0 the function is reflected over the y-axis.
h: h is a horizontal translation.
k: k is a vertical translation.
There are other possible transformations, but these are the basics.
For `f(x)=root(3)(x)` and `g(x)=root(3)(x-6)` we can see that g(x) is a transformation of f(x), and that the transformation is of the "h" type. `g(x)=root(3)(x-h)` where h=6: this is a horizontal translation -- g(x) looks like f(x) shifted 6 units to the right.
The graph of f(x) in red; the graph of g(x) in green: