Difference between revisions of "1995 AHSME Problems/Problem 12"
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Revision as of 12:59, 5 July 2013
Contents
[hide]Problem
Let be a linear function with the properties that and . Which of the following is true?
Solution 1
A linear function has the property that either for all , or for all . Since , . Since , . And if for , then is a constant function. Since ,
Solution 2
If is a linear function, the statement states that the slope of the line is nonnegative: it is either positive or zero.
Similarly, the statement states that the slope of the line is nonpositive: it is either negative or zero.
Since the slope of a linear function can only have one value, it must be zero, and thus the function is a constant. The statement tells us that the value of the constant is , and thus that . This leads to
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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