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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.10 - Solution

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The graphs of and both have vertices located at the origin, so we know that there haven't been any translations. However, is upside down and somewhat stretched. The fact that is upside down means that it has been reflected in the -axis. This means is a negative number. Let's assume, temporarily, that In this case, we would only change the sign of the graph's -values, taking us from the graph of to the graph of shown below.

To get from the graph of to the graph of we need to stretch away from the -axis. Let's look at a point on each graph with the same -values and compare their -values.

The graph of passes through and the graph of passes through This means that the -values in have been stretched by a factor of Therefore, to get both a reflection in the -axis and a stretch of we must have that