Difference between revisions of "2014 AMC 12A Problems/Problem 24"
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==Solution== | ==Solution== | ||
− | 1. Draw the graph of f_0(x) by dividing the domain into three parts. | + | 1. Draw the graph of <math>f_0(x)</math> by dividing the domain into three parts. |
2. Look at the recursive rule. Take absolute of the previous function and down by 1 to get the next function. | 2. Look at the recursive rule. Take absolute of the previous function and down by 1 to get the next function. | ||
− | 3. Count the x intercepts of the each function and find the pattern | + | 3. Count the x intercepts of the each function and find the pattern. |
+ | The pattern turns out to be <math>3n+1</math> solutions, and the answer is thus <math>\textbf{(C) }301\qquad</math>. | ||
(Revised by Flamedragon) | (Revised by Flamedragon) | ||
Revision as of 12:27, 13 February 2014
Problem
Let , and for
, let
. For how many values of
is
?
Solution
1. Draw the graph of by dividing the domain into three parts.
2. Look at the recursive rule. Take absolute of the previous function and down by 1 to get the next function.
3. Count the x intercepts of the each function and find the pattern.
The pattern turns out to be solutions, and the answer is thus
.
(Revised by Flamedragon)
See Also
2014 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.