<p>hi guys. i am having trouble answering this question. can anyone explain this for me? thanks :) </p>
<p>It would help if you didn’t use a potato to take that picture. But from what I can see, what does f(x+ 5)=f(x) mean? It means f @ x is the exact same value at x+5. So f has the same value at x=1&6, 2&7, 3&8, etc.</p>
<p>Considering that, how many times does f=0 on that graph? So how many times does f=0 from 0 to 12? That should be your answer.</p>
<p>thanks for the reply. the answer is 9 but I still dont get it. the question is in page 369, number 8 of the blue book by the way</p>
<p>What the f(x+5)=f(x) part is trying to tell you is that the function repeats itself. If you plug in values for x, you’ll discover that f(6)=f(1), f(7)=f(2), and so on. You can stretch it further by saying f(12)=f(7), f(13)=f(8), and so on. If you haven’t noticed yet, the function has a period (is that what they call it?) of 5. For the graph in the question, you can see that f(x) equals zero at x= 1.5, 2.5, 3 and 4.5. Using the f(x=5)=f(x) property, we can say that f(x) equals zero also at 6.5 (1.5+5), 7.5(2.5+5), 8 and 9.5. Adding an additional five to all the points, we deduce that f(x) equals 0 at 11.5, 12.5, 13 and 14.5, too. Now all you have to do is count the points that are between 0 and 12, which is 9.</p>