Two urns each contain green balls and blue balls. urn i contains 4 greenballs and 6 blue balls, and urn ii contains 6 green ball
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This chart may seem confusing, but it's not too bad once you get the hang of it. It is known as a mileage chart and it shows the distances between any two cities of this current list.
For example, the distance between Bedford and Cambridge is 29 miles because of the "29" in the very top block. This is the intersection between the "bedford" column and the "cambridge" row. Another example: The distance from Cambridge to Haverhill is 48 miles. Look in the "cambridge" column and the "haverhill" row.
With this in mind, we just need to look at the right rows and columns to find the distances to add up. See the set of attached images below. Figure 1 shows me marking the "cambridge" column and the "royston" row. In this row and column combo is the number 13. So the distance between these two cities is 13 miles.
Then onto figure 2 which shows the distance between Royston and Huntingdon is 21 miles. Figure 3 shows the distance from Huntingdon to Cambridge is 15 miles.
Adding the distances gives: 13+21+15 = 49
So that is why the total round trip distance is 49 miles.
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.