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

1 Answer
Noah G
Apr 15, 2018

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!

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