What is the meaning of the last equation in words?

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Homework Help Overview

The discussion revolves around a piecewise function defined over specific intervals and its periodicity. Participants are exploring the implications of the equation f(x) = f(x+8) and its meaning in the context of the function's behavior.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to interpret the meaning of the periodicity condition and how it affects the function. Questions about sketching the graph over multiple periods and determining the function's parity are also raised.

Discussion Status

Some participants have provided hints and guidance regarding the periodic nature of the function and the criteria for determining if it is odd or even. There is an ongoing exploration of the implications of the periodicity and the function's definition.

Contextual Notes

Participants are reminded of forum rules requiring attempts at answering questions before receiving assistance. There is also a hint provided regarding evaluating the function at specific points, which may influence understanding of the periodicity.

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Homework Statement


the function decribed by
f(x) = (2, -2<x<2
= (0, 2<x<6

and f(x) = f(x+8)

Q1, what does the last equation mean in words?
Q2, how do i sketch the graph of the function f(x) over 3 periods?
Q4, is it odd or even?

Homework Equations





The Attempt at a Solution

 
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The rules of the forum are that you need to attempt to answer these before anyone can help. It just has to be an attempt. What would a function that satisfies f(x)=f(x+8) look like? Any opinions?
 
Ma77yD182 said:

Homework Statement


the function decribed by
f(x) = (2, -2<x<2
= (0, 2<x<6

and f(x) = f(x+8)

Q1, what does the last equation mean in words?
Q2, how do i sketch the graph of the function f(x) over 3 periods?
Q4, is it odd or even?

Homework Equations





The Attempt at a Solution

Can you use those to find f(7)? Hint: 7= -1+ 8.
 
It's period will become 8 (obvious).
And determine odd or even function:
if f(-x) = f(x) then even function
if f(-x) = -f(x) then odd function.
 

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