Question

The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range but not the domain of the transformed function is the same as that of the parent function. The domain but not the range of the transformed function is the same as that of the parent function.

Answer 1

D. The domain but not the range of the transformed function is the same as that of the parent function.

Explanation:

We are given,

The function
`f(x)=|x|` is reflected across x-axis, which gives
`-|x|`.

And then the function is translated to the right by 6 units, which gives
`-|x-6|`.

Thus, the transformed function is
`g(x)=-|x-6|`

So, from the graph shown below, we get,

Domain of both the functions f(x) and g(x) is set of all real numbers.

Range of f(x) is
`\y\geq 0\`.

But, Range of g(x) is
`\y\leq 0\`.

Hence, the correct option is,

D. The domain but not the range of the transformed function is the same as that of the parent function.

Answer 2

Answer: The domain but not the range of the transformed function is the same as that of the parent function.

The domain is still D: x∈R
but the range of parent function is f(D): y∈<0;∞) and the range of the transformed function is g(D): y∈(-∞;0>



"Non nobis Domine, non nobis, sed Nomini tuo da gloriam."


Regards M.Y.