Graph & Analyze Fourier Coefficient of Periodic Function

[longball]

A periodic function f(x) has period 2 and is defined as

f(x) = -2.4 (x+1) ,-1 ≤ x < 0
2.4 (1-x) , 0 < x ≤ 1

with f(x+2) = f(x) for all x

sketch the graph of f(x) over the interval (-4, +4) and determine the Fourier coefficient Ao.

I really don't know where to start with this question any help would be great.

 

[lanedance]

hi longball, welcome to pf - where are you stuck? can you sketch the graph

 

[longball]

no i don't know where to start with the graph. I am guessing that the graph is to take the shape of a saw tooth, could be wrong though. i also do not understand what the (x+1) (x-1) stands for

 

[lanedance]

start with the first part of the graph
f(x) = -2.4 (x+1) ,-1 ≤ x < 0

multiplying out the brackets gives
f(x) = (-2.4)*x - 2.4
this is the equation of a straight line, can you plot it on the x interval from -1 to 0?

do similar for
f(x) = (-2.4)*x + 2.4
and plot it for on the x interval from 0 to 1