- #1

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?