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? a)both the domain and range of the transformed function are the same as those of the parent function.
b(neither the domain nor the range of the transformed function are the same as those of the parent function.
c)the range but not the domain of the transformed function is the same as that of the parent function.
d)the domain but not the range 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 D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) translated horizontally to the right  by h units,

 then the new function g(x) = f(x - h)

- The domain of a function is set of the values of x which make

  the function defined

- The range is the set values of y that corresponding with the domain

- The domain of the function f(x) = IxI is the set of all real numbers

∴ The domain of f(x) is {x : x ∈ R}

- The range of  the function f(x) = IxI is the set of all real numbers

  greater than or equal 0

∴ The range f(x) = {y : y ≥ 0}

∵ f(x) reflected across the x-axis, then it will be change to g(x) = -IxI

∴ All the y-coordinates of the point on the function will be change

  from positive values to negative values

∵ The rang of f(x) is {y : y ≥ 0}

∴ The range of g(x) is {y : y ≤ 0}

∵ After the reflection the function translated 6 units to the right

∴ The x will change to x - 6

∴ The function will be h(x) = -Ix - 6I

- There is no values of x make h(x) undefined, then its domain is

  set of all real number

∴ The domain of h(x) is {x : x ∈ R}

∵ The domain of f(x) is {x : x ∈ R}

∵ The range of h(x) is the same the range of g(x)

∴ The range of h(x) is {y : y ≤ 0}

- f(x) and h(x) have same domains and different ranges

∴ The correct statement is: The domain but not the range of the

   transformed function is the same as that of the parent function

- Look to the attached graph for more understanding

# The red graph is f(x)

# The blue graph is h(x)

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540