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opus
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Homework Statement
Consider ##u\left(x\right)=2\left[\frac{-x}{4}\right]##
(a) Find the length of the individual line segments of the function,
(b) Find the positive vertical separation between line segments.
Homework Equations
The output of Greatest Integer Functions are always integers.
The Attempt at a Solution
I'm honestly confused about this whole situation.
Length:
The text states that the coefficient of x within the greatest integer symbols is the length of the individual line segments of the graph.
In ##u\left(x\right)=2\left[\frac{-x}{4}\right]##, the coefficient of x is ##\frac{-1}{4}##.
However, the solution for the length of the graph states that length=4.
It explains this by stating that there's a decrease of 1 for every increase of 4 in the variable x.
This would make sense if we were talking about the slope of a line, but it doesn't make any sense at all in this context.
And since we're talking about the length of a line segment, does the negation matter?
Vertical Separation:
The text states that the coefficient of the greatest integer function is the positive vertical separation between line segments.
This is a straight forward statement, and the vertical separation=2, but I don't see why this leading coefficient determines this.
Can anyone help me get a better idea of what is going on with the graphs of these functions?