Answer:
The domain but not the range of the transformed function is the same as that of the parent function ⇒ answer D
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)