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Answer: D) Reflect over x-axis
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Explanation:
When we do this type of reflection, a point like (1,2) moves to (1,-2).
As another example, something like (5,-7) moves to (5,7)
The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.
We can say that as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.
If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.
There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is