Question

The domain of the function g(x) is -1<x<6 and the range is -5<y<10.
Find the domain and range of the following given functions.

a). the domain of y=g(x-4) is?
b.) the range of y=g(x)+2 is?

Answer 1

a )The domain is the set of numbers you plug into g. Here, the number you plug into g(x) x needs to be between −1 and 6 Since the number you're plugging into g is x−4, this means you need −1<x−4<6, which is equivalent to 3<x<10

The range is the set of values that the function g

takes; since g(x−4) is simply a value of g for each input x, the range of the new function is the same as the range of the old function.

b) y - 2 =g(x)

since now the value plugged into g remains same but the output y is 2 added to the initial fucntion g

the range becomes -5<y-2<10 => -3<y< 12