plotting a function

[flyryd]

the problem:

f(x) = 1−((x^2)/4), for−2 ≤ x ≤ 2
with f(x+3) = f(x)

the Question: plot the function.



i can do the first line, but i do not understand what the second line means.
does it mean f(x+3) = f(x) = 1−((x^2)/4), for−2 ≤ x ≤ 2 ?

how does f(x+3) = f(x) ???
and what does plot the function imply? f(x+3)? f(x)?

thanks in advance

 

[HallsofIvy]

The function you want to plot is y= f(x), not f(x+ 3). Saying that "f(x)= f(x+ 3)" means that f is periodic with period 3- its graph repeats.

However, the numbers you give here don't jibe. The first section on which you are given a specific formula, \(\displaystyle -2< x< 2\), has length 4 while "f(x+3)= f(x) gives period 3. That means, for example, that the first formula gives f(1)= 1- 1/4= 3/4 while "f(x+3)= f(3)" gives f(1)= f(-2+3)= f(-2)= 1- 4/4= 0.
Check the problem again to see if you have not copied something wrong.

 

[Dale10101]

Also confused

Started by separating the the operator from the overall function:

$\begin{array}{l}
f() = 1 - \frac{{{{()}^2}}}{4}\\
\\
f(x) = 1 - \frac{{{{(x)}^2}}}{4}\\
\\
f(x + 3) = 1 - \frac{{{{(x + 3)}^2}}}{4}\\
\\
f(x) = f(x + 3) = > \\
\\
1 - \frac{{{{(x)}^2}}}{4} = 1 - \frac{{{{(x + 3)}^2}}}{4} = > \\
\\
x = \frac{{ - 3}}{2}\\


\end{array}$

The result is a solution not a function. I am not sure what the problem is asking for either.

Am starting to see what HOI is saying.

If the problem was

f(x) = 1−((x^2)/4), for−2 ≤ x ≤ 2 with f(x+4) = f(x)

you could say f(x) =f(x+4), i.e. f at x has the same value as f at x+4 ....in that case how would you write, notationally, a non-periodic function as a periodic function. Interesting problem.