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### Assignment 6

Draw the graph of

### Solution

We apply the definition of the absolute value to both terms.

if , so if or (see also assignment 4). Call this interval A.

if . Call this interval B.

if . Call this interval C.

if . Call this interval D.

To draw the graph we distinguish the following intervals.

, this is the union of the intervals A and D, briefly AD.

, this is the union of the intervals B and D, briefly BD.

, this is the union of the intervals B and C, briefly BC.

, this is the union of the intervals A and C, briefly AC.

For AD we have:

For BD we have:

For BC we have:

For AC we have:

The resulting graph is built up by portions of four different parabolas. The first part intercepts and has a minimum for . Calculate the same characteristics for the other parabolas and explain them based on the chart. Note that the graph fits the given function.

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