# Thread: Trying to understand these functions...

1. ## Trying to understand these functions...

I have two functions that I'm not quite sure how to deal with, if I could imagine their graphs I'd be fine but I can't I've looked everywhere for a simple explanation, now I'm looking here =]

--------sin(pi*x/2)--------[0,2]
f(x) = { 0----------------[2,4]
--------f(x+4)

I have no idea what the square brackets are trying to tell me here =/

--------0---------1 < x < 0
f(x) = { 1/2-------x=n--------nEz
--------1--------0 < x < 1
--------f(x+2)

Again, I'm not quite sure how to read this. Anyone help me??

2. Hello, Stuckasaurus!

$\displaystyle f(x) \;=\;\begin{Bmatrix}\sin\left(\frac{\pi}{2}x\right ) & [0,2] \\ \\[-4mm] 0 & [2,4] \\ f(x+4) & {\color{red}?}\end{Bmatrix}$
I'm not sure what that third entry means.
It probably means that this graph is repeated over and over,
. . but I'll graph just one "cycle".

The brackets indicate intervals.
. . $\displaystyle [0,2]$ means: .$\displaystyle 0 \leq x \leq 2$

Brackets mean the endpoints are included.

If the endpoints are not included, parentheses are used.
. . $\displaystyle (1,3)$ means: .$\displaystyle 1 < x < 3$

And, yes, they can be "mixed".
. . $\displaystyle (0, 4]$ means: .$\displaystyle 0 < x \leq 4$

This problem says:

If $\displaystyle 0 \leq x \leq 2$, the graph is a sine function: .$\displaystyle y \:=\:\sin\left(\frac{\pi}{2}x\right)$

If $\displaystyle 2 \leq x \leq 4$, the graph is $\displaystyle y \:=\:0$ ... the x-axis.

The graph looks like this:
Code:
        |
1+       *
|   *       *
| *           *
|*             *
|
- - * - - - - - - - * * * * * * * * * - -
|               2               4

$\displaystyle f(x) \;=\;\begin{Bmatrix}0 & -1 < x < 0 \\ \\[-4mm] \frac{1}{2} & x \in Z \\ \\[-4mm] 1 & 0 < x < 1 \\ f(x+2) & {\color{red}?}\end{Bmatrix}$

This function says:

If $\displaystyle x$ is between -1 and 0, the graph is $\displaystyle y = 0$, the x-axis.

If $\displaystyle x$ is an integer, the graph is ½.

If $\displaystyle x$ is between 0 and 1, the graph is $\displaystyle y = 1$

And the graph looks like this:
Code:
                |
1o=======o
|
*
|
- - o=======o - - - + - -
-1       |       1

3. Wow, you're like.. better than my lecturer! Thanks soooo much =]