Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
7. Graphing Absolute Value Functions
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Exercise 21 Page 160

What are the slopes of the arms of the functions and

see solution.

Practice makes perfect
The graphs of the absolute value functions 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