The function graphed is reflected across the x-axis to create a new function.(Absolute function opening up, vertex at (4,2))Which is true about domain and range of the function?
C.
When a function is reflected across the x-axis, the y-coordinates of all points on the original graph are negated. Therefore, the absolute function with a vertex at (4,2) would be reflected across the x-axis as shown below:
The original function has a domain of all real numbers and a range of y ≥ 0 since the absolute value of any real number is non-negative.
When the function is reflected across the x-axis, the domain remains the same, but the range is negated. Specifically, the range of the reflected function is y ≤ 0 since all y-coordinates are negated. Therefore, the domain of the reflected function is all real numbers, and the range is y ≤ 0.
In summary, the function reflected across the x-axis has a domain of all real numbers and a range of y ≤ 0.
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