Difference between revisions of "2024 AIME I Problems/Problem 12"
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If we graph <math>4g(f(x))</math>, we see it forms a sawtooth graph that oscillates between <math>0</math> and <math>1</math> (for values of <math>x</math> between <math>-1</math> and <math>1</math>, which is true because the arguments are between <math>-1</math> and <math>1</math>). Thus by precariously drawing the graph of the two functions in the square bounded by <math>(0,0)</math>, <math>(0,1)</math>, <math>(1,1)</math>, and <math>(1,0)</math>, and hand-counting each of the intersections, we get <math>\boxed{384}</math> | If we graph <math>4g(f(x))</math>, we see it forms a sawtooth graph that oscillates between <math>0</math> and <math>1</math> (for values of <math>x</math> between <math>-1</math> and <math>1</math>, which is true because the arguments are between <math>-1</math> and <math>1</math>). Thus by precariously drawing the graph of the two functions in the square bounded by <math>(0,0)</math>, <math>(0,1)</math>, <math>(1,1)</math>, and <math>(1,0)</math>, and hand-counting each of the intersections, we get <math>\boxed{384}</math> | ||
===Note=== | ===Note=== | ||
− | While this solution might seem unreliable (it probably is), the only parts where counting the intersection might be tricky is near | + | While this solution might seem unreliable (it probably is), the only parts where counting the intersection might be tricky is near <math>(1,1)</math>. Make sure to count them as two points and not one, or you'll get <math>383</math>. |
==See also== | ==See also== |
Revision as of 19:41, 2 February 2024
Contents
[hide]Problem
Define and . Find the number of intersections of the graphs of
Solution 1 (BASH, DO NOT ATTEMPT IF INSUFFICIENT TIME)
If we graph , we see it forms a sawtooth graph that oscillates between and (for values of between and , which is true because the arguments are between and ). Thus by precariously drawing the graph of the two functions in the square bounded by , , , and , and hand-counting each of the intersections, we get
Note
While this solution might seem unreliable (it probably is), the only parts where counting the intersection might be tricky is near . Make sure to count them as two points and not one, or you'll get .
See also
2024 AIME I (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 | ||
All AIME Problems and Solutions |
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