Starsailor Posted October 10, 2005 Share Posted October 10, 2005 Hello, I wonder if any of you could explain the answer to a question that has left me rather stumped. It's a past question from the UKMT Senior Challenge and I know I should be able to do it, but I don't even understand what it wants me to do Anyway, enough waffling... "The graph of y= l f(x) l is shown ( f(x)= x^2). Given that the graph of y= f(x) is a continuous curve, how many different possibilities are there for the graph of y=f(x)?" What does it want me to do?! Cheers, Michael Link to comment Share on other sites More sharing options...
Dave Posted October 10, 2005 Share Posted October 10, 2005 Do you mean "possibilities are there for the graph of y = |f(x)|"? Link to comment Share on other sites More sharing options...
Starsailor Posted October 10, 2005 Author Share Posted October 10, 2005 Do you mean "possibilities are there for the graph of y = |f(x)|"? No; Perhaps it would be best to see the question as it is written. Link to comment Share on other sites More sharing options...
Dave Posted October 10, 2005 Share Posted October 10, 2005 Ah, I get it. It wants to know what f(x) could possibly look like so that the graph of |f(x)| looks the same. For example, you could have f(x) look exactly like the graph. Or, you could have the first "lump" below the x-axis with the second above the x-axis. Or... Link to comment Share on other sites More sharing options...
jcarlson Posted October 11, 2005 Share Posted October 11, 2005 Think of it this way. Break the graph of |f(x)| into 4 segments, where the segments are divided by where the graph touches the x-axis. Now, for the graph of f(x), each of those segments can either look like it does for |f(x)|, or it can be the reflection of |f(x)| over the x-axis, because both will look the same when you plot |f(x)|. Thus f(x) has 2 possible curves for each of 4 segments which are independent of the other segments. now use probablility to find the number of possible graphs of f(x) or just count them. Link to comment Share on other sites More sharing options...
Starsailor Posted October 13, 2005 Author Share Posted October 13, 2005 Ah right. Cheers Michael Link to comment Share on other sites More sharing options...
matt grime Posted October 13, 2005 Share Posted October 13, 2005 now use probablility probability???? Link to comment Share on other sites More sharing options...
Dave Posted October 13, 2005 Share Posted October 13, 2005 Perhaps combinatorics would be a slightly better choice of words Link to comment Share on other sites More sharing options...
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