vivektripathi wrote:
If -2<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x?
(A) 5 <= y-x <= 6
(B) 1 <= y-x <= 5
(C) 1 <= y-x <= 6
(D) 5 <= y-x <= 10
(E) 1 <= y-x <= 10
"Range of all possible values" for \(y - x\) is just another way of asking about the expression's minimum value and maximum value.
Minimum and maximum of \(y - x\)? Where
\(-2 \leq x \leq 2\)
\(3 \leq y \leq 8\)
To find the smallest (minimum) value for \(y - x\), you can either:
1) Keep order of subtraction in mind, and find two same-sign values that are close together (which omits -2 from calculation). Two positives for y, one for x. Closest: 3 and 2. Answer is 1. Or
2) Test all four cases
8 - 2 = 6
8 - (-2) = 10
3 - 2 = 1
3 - (-2) = 5
Minimum value of \(y - x\) = 1
Maximum?
1. Same things to keep in mind, but look for opposite-sign values that are large (or larger, if there are two negs. or two positives). Negative subtracted from positive = addition. Larger positive for y is 8. Only negative for x is -2. Answer is 10. Or
2. Test four cases
8 - 2 = 6
8 - (-2) = 10
3 - 2 = 1
3 - (-2) = 5
Maximum value of \(y - x\) = 10
Answer: \(1 \leq(y -x) \leq10\)
I tested all eight cases, checked my work, and time was
well under a minute (so maybe what looks like the longest way isn't).
Answer E
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