Question

The domain of f(x) is −6 ≤ x ≤ 8 and the range is 6 ≤ y ≤ 12. If g(x) = 3f(x − 6), what is the domain and range of g(x) ?

The
domain 0 ≤ x≤ 14
range 18 ≤ y≤ 36
but I'm not sure how to solve to get to these answers

Answer 1

When dealing with transformations I find it useful to use the following equation:

`(m/b + c, an + d)`

Where `(m, n)` is the point and the function is `g(x) =afb(x- c) + d`. We can apply this to the endpoints of the domain and range to determine the new endpoints. Our two points will be `(-6, 6)` and `(8, 12)`. Our parameters will be `a = 3`, `b = 1`, `c = 6` and `d = 0`.

`(-6 + 6, 3(6)) = (0, 18)`
`(8 + 6, 3(12)) = (14,36)`

Thus our new domain will be `0 ≤ x ≤ 14` and our new range will be `18 ≤ y≤ 36`, just as your answers said.

Hopefully this helps!