*If 0 < x _< 8, and -1 _< y _< 3, which of the following gives the set of all possible values of xy? PS (< means less than or equal to).
A) xy=4
B) 0 _< xy _< 24
C) -1 _< xy _< 11
D) -1 _< xy _< 24
E) -8 _< xy _< 24*
What is the logic behind the correctness of answer E?
Multiply the numbers you’re given together in all different combos xy.
0, 8, -1, 3
0 x -1 = 0
0 x 3 = 0
-1 x 8 = -8
3 x 8 = 24
What’s the highest? The lowest?
Thank you, I know this. I just don’t get what exactly happens when x is multiplied by y.
Every number in the x range is multiplied by every number in the y range. This results in a lot of numbers as answers. Many of them are zero, as zero is included in both of the ranges and anything multiplied by it will be zero.
But as for why you only need to care about the outer numbers:
-1 times everything in the other range results in answers of 0, -1, -2, -3, -4, -5, -6, -7, and -8.
The next number from the y range is 0. All of those answers are zero. None are lower than -8 from the first range.
The next number is 1. Will 1 times anything positive result in a lower number than -8?
Feel free to write out every answer that x*y generates…you’ll see that the lowest one should be -8 and the highest should be 24. All the other answers will be in that range. Which makes sense, as the numbers that get you the highest and lowest answers are also the extremes of their sets. The numbers in the middle will get you answers in the middle.
THANKS SO MUCH!!