2003 AMC 10A Problems/Problem 6
Problem
Define to be for all real numbers and . Which of the following statements is not true?
for all and
for all and
for all
for all
if
Solution
Examining statement C:
when , but statement D says that it does for all .
Therefore the statement that is not true is " for all "
Alternatively, consider that the given "heart function" is actually the definition of the distance between two points. Examining all of the statements, only C is not necessarily true; if c is negative, the distance between c and 0 is the absolute value of c, not c itself, because distance is always nonnegative.
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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