1. ## f(x+5) = f(x)

The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x between 0 and 12?

http://img187.imageshack.us/img187/4666/dsc00054i.jpg

a. 8
b. 9
c. 10
d. 11
e. 12

thanks

also whats a period graph of function? hows it related to the question?

thanks

2. ## Periodic function

Hello aeroflix
Originally Posted by aeroflix
The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x between 0 and 12?

http://img187.imageshack.us/img187/4666/dsc00054i.jpg

a. 8
b. 9
c. 10
d. 11
e. 12

thanks

also whats a period graph of function? hows it related to the question?

thanks
A periodic function is one whose values are repeated at regular intervals or periods. On the graph of the function, the period itself is the horizontal distance between two consecutive corresponding points.

If $f$ is such that $f(x+5) = f(x)$ for all values of $x$ then $f$ is periodic with period $5$. This means that the graph repeats every $5$ units horizontally.

To find where $f(x) = 0$, we need to know where the graph crosses the $x$-axis. Between $x = 0$ and $x = 5$, the graph cuts the $x$-axis $4$ times; so it will cut it another $4$ times between $5$ and $10$. (That's $8$ so far.)

Between $0$ and $2$, the graph crosses the $x$-axis just once; so it will cross once between $10$ and $12$.

So there are $9$ values of $x$ between $0$ and $12$ altogether.

3. from 1 to 5 : 4
from 6 to 10 : 4
from 11 to 12 : 1

4 + 4 + 1 = 9

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