Difference between revisions of "2014 AMC 12A Problems/Problem 24"

(Solution)
(Solution)
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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
  
(Revised by William Chi)
+
(Revised by Flamedragon)
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2014|ab=A|num-b=23|num-a=25}}
 
{{AMC12 box|year=2014|ab=A|num-b=23|num-a=25}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:36, 9 February 2014

Problem

Let $f_0(x)=x+|x-100|-|x+100|$, and for $n\geq 1$, let $f_n(x)=|f_{n-1}(x)|-1$. For how many values of $x$ is $f_{100}(x)=0$?

$\textbf{(A) }299\qquad \textbf{(B) }300\qquad \textbf{(C) }301\qquad \textbf{(D) }302\qquad \textbf{(E) }303\qquad$

Solution

1. Draw the graph of f_0(x) 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

(Revised by Flamedragon)

See Also

2014 AMC 12A (ProblemsAnswer KeyResources)
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

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