Difference between revisions of "1982 AHSME Problems/Problem 19"
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draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); | draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); | ||
draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); | draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); | ||
− | label("$x$",(xMax,0), | + | label("$x$",(xMax,0),(2,0)); |
− | label("$y$",(0,yMax), | + | label("$y$",(0,yMax),(0,2)); |
pair A[]; | pair A[]; |
Latest revision as of 12:26, 13 September 2021
Problem
Let for
. The sum of the largest and smallest values of
is
Solution
Note that at one of the three absolute values is equal to
Without using absolute values, we rewrite as a piecewise function:
which simplifies to
The graph of
is shown below.
The largest value of
is
and the smallest value of
is
So, their sum is
~MRENTHUSIASM
See Also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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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