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2 answers:
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This is an example of a piecewise defined function. It means that the function has not a unique formula to represent it, but it depends on "where" you want to compute it.
So, if you choose any input , you have two alternative:
- If
(i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen (
)
- If
, the ouput will be -1.
So, let's forget about for a moment. For any input
you choose, the answer is
. The graph of this function is the bisector of the second and fourth quadrant.
Now remember that there is our special case: you have to "carve a hole" in our line, at , and assing to this point the value -1, instead of what we would expect, i.e. -3.
So, the graph of this function is the line , except for one point (
), where we reassign the value to be -1.
Given:
The scale factor between two circles is .
To find:
The ratio of their areas.
Solution:
We know that, all circles are similar.
The ratio of the areas of similar figures is equal to the ratio of squares of their corresponding sides or equal to the square of ratio of their corresponding sides.
The scale factor is the ratio of the corresponding sides.
Ratio of areas of circles = Square of scale factor between two circles
Therefore, the correct option is D.