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**

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